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1

Mishra, Manish, e Basudev Pattanayak. "Principal series component of Gelfand-Graev representation". Proceedings of the American Mathematical Society 149, n. 11 (5 agosto 2021): 4955–62. http://dx.doi.org/10.1090/proc/15642.

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2

Chan, Kei Yuen, e Gordan Savin. "Iwahori component of the Gelfand–Graev representation". Mathematische Zeitschrift 288, n. 1-2 (23 marzo 2017): 125–33. http://dx.doi.org/10.1007/s00209-017-1882-3.

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3

Breeding-Allison, Jeffery, e Julianne Rainbolt. "The Gelfand–Graev representation of GSp(4,𝔽q)". Communications in Algebra 47, n. 2 (17 gennaio 2019): 560–84. http://dx.doi.org/10.1080/00927872.2018.1485228.

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4

Rainbolt, Julianne G. "The Gelfand–Graev Representation of U(3,q)". Journal of Algebra 188, n. 2 (febbraio 1997): 648–85. http://dx.doi.org/10.1006/jabr.1996.6860.

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5

TAYLOR, JAY. "GENERALIZED GELFAND–GRAEV REPRESENTATIONS IN SMALL CHARACTERISTICS". Nagoya Mathematical Journal 224, n. 1 (9 settembre 2016): 93–167. http://dx.doi.org/10.1017/nmj.2016.33.

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Abstract (sommario):
Let $\mathbf{G}$ be a connected reductive algebraic group over an algebraic closure $\overline{\mathbb{F}_{p}}$ of the finite field of prime order $p$ and let $F:\mathbf{G}\rightarrow \mathbf{G}$ be a Frobenius endomorphism with $G=\mathbf{G}^{F}$ the corresponding $\mathbb{F}_{q}$-rational structure. One of the strongest links we have between the representation theory of $G$ and the geometry of the unipotent conjugacy classes of $\mathbf{G}$ is a formula, due to Lusztig (Adv. Math. 94(2) (1992), 139–179), which decomposes Kawanaka’s Generalized Gelfand–Graev Representations (GGGRs) in terms of characteristic functions of intersection cohomology complexes defined on the closure of a unipotent class. Unfortunately, the formula given in Lusztig (Adv. Math. 94(2) (1992), 139–179) is only valid under the assumption that $p$ is large enough. In this article, we show that Lusztig’s formula for GGGRs holds under the much milder assumption that $p$ is an acceptable prime for $\mathbf{G}$ ($p$ very good is sufficient but not necessary). As an application we show that every irreducible character of $G$, respectively, character sheaf of $\mathbf{G}$, has a unique wave front set, respectively, unipotent support, whenever $p$ is good for $\mathbf{G}$.
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Curtis, Charles W., e Ken-ichi Shinoda. "Unitary Kloosterman Sums and the Gelfand–Graev Representation of GL2". Journal of Algebra 216, n. 2 (giugno 1999): 431–47. http://dx.doi.org/10.1006/jabr.1998.7807.

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7

Kochubei, Anatoly N., e Yuri Kondratiev. "Representations of the infinite-dimensional p-adic affine group". Infinite Dimensional Analysis, Quantum Probability and Related Topics 23, n. 01 (marzo 2020): 2050002. http://dx.doi.org/10.1142/s0219025720500022.

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We introduce an infinite-dimensional [Formula: see text]-adic affine group and construct its irreducible unitary representation. Our approach follows the one used by Vershik, Gelfand and Graev for the diffeomorphism group, but with modifications made necessary by the fact that the group does not act on the phase space. However, it is possible to define its action on some classes of functions.
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8

HIROSHI, ANDO. "ON THE LOCAL STRUCTURE OF THE REPRESENTATION OF A LOCAL GAUGE GROUP". Infinite Dimensional Analysis, Quantum Probability and Related Topics 13, n. 02 (giugno 2010): 223–42. http://dx.doi.org/10.1142/s0219025710004036.

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We discuss the local structure of the net [Formula: see text] of von Neumann algebras generated by a representation of a local gauge group [Formula: see text]. Our discussion is independent of the singularity of spectral measures, which has been discussed by many authors since the pioneering work of Gelfand–Graev–Veršic. We show that, for type (S) operators UA,b, second quantized operators with some twists, the commutativity only with those U(ψ) is sufficient for the triviality of them, where ψ belongs to an arbitrary (small) neighborhood of constant function 1. Some properties of 1-cocycles for the representation V : ψ ↦ Ad ψ are also discussed.
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9

Curtis, Charles W. "On the irreducible components of a Gelfand–Graev representation of a finite Chevalley group". Pacific Journal of Mathematics 307, n. 1 (8 agosto 2020): 109–19. http://dx.doi.org/10.2140/pjm.2020.307.109.

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Bonnafé, Cédric, e Raphaël Rouquier. "Coxeter Orbits and Modular Representations". Nagoya Mathematical Journal 183 (2006): 1–34. http://dx.doi.org/10.1017/s0027763000009259.

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AbstractWe study the modular representations of finite groups of Lie type arising in the cohomology of certain quotients of Deligne-Lusztig varieties associated with Coxeter elements. These quotients are related to Gelfand-Graev representations and we present a conjecture on the Deligne-Lusztig restriction of Gelfand-Graev representations. We prove the conjecture for restriction to a Coxeter torus. We deduce a proof of Brouée’s conjecture on equivalences of derived categories arising from Deligne-Lusztig varieties, for a split group of type An and a Coxeter element. Our study is based on Lusztig’s work in characteristic 0 [Lu2].
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11

SHINODA, KENICHI, e ILKNUR TULUNAY. "REPRESENTATIONS OF THE HECKE ALGEBRA FOR GL4(q)". Journal of Algebra and Its Applications 04, n. 06 (dicembre 2005): 631–44. http://dx.doi.org/10.1142/s0219498805001459.

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In this article, we explicitly calculated the values of the representations of the Hecke algebra [Formula: see text], associated with a Gelfand–Graev character of GL 4(q), at some of the standard basis elements.
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12

Clarke, Matthew C. "On the endomorphism algebra of generalised Gelfand-Graev representations". Transactions of the American Mathematical Society 364, n. 10 (1 ottobre 2012): 5509–24. http://dx.doi.org/10.1090/s0002-9947-2012-05543-7.

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13

Panov, A. N. "Representations of Gelfand–Graev Type for the Unitriangular Group". Journal of Mathematical Sciences 206, n. 5 (26 marzo 2015): 570–82. http://dx.doi.org/10.1007/s10958-015-2334-4.

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14

Rainbolt, Julianne G. "The Generalized Gelfand–Graev Representations of U(3,q)". Journal of Algebra 202, n. 1 (aprile 1998): 44–71. http://dx.doi.org/10.1006/jabr.1997.7250.

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15

Bonnafé, Cédric, e Radha Kessar. "On the endomorphism algebras of modular Gelfand–Graev representations". Journal of Algebra 320, n. 7 (ottobre 2008): 2847–70. http://dx.doi.org/10.1016/j.jalgebra.2008.05.029.

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16

RAINBOLT, JULIANNE G. "WEYL GROUPS AND BASIS ELEMENTS OF HECKE ALGEBRAS OF GELFAND–GRAEV REPRESENTATIONS". Journal of Algebra and Its Applications 10, n. 05 (ottobre 2011): 849–64. http://dx.doi.org/10.1142/s0219498811005002.

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The initial section of this article provides illustrative examples on two ways to construct the Weyl group of a finite group of Lie type. These examples provide the background for a comparison of the elements in the Weyl groups of GL(n, q) and U(n, q) that are used in the construction of the standard bases of the Hecke algebras of the Gelfand–Graev representations of GL(n, q) and U(n, q). Using a theorem of Steinberg, a connection between a theoretic description of bases of these Hecke algebras and a combinatorial description of these bases is provided. This leads to an algorithmic method for generating bases of the Hecke algebras of the Gelfand–Graev representations of GL(n, q) and U(n, q).
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17

Dong, Junbin, e Gao Yang. "Geck's conjecture and the generalized Gelfand-Graev representations in bad characteristic". Advances in Mathematics 377 (gennaio 2021): 107482. http://dx.doi.org/10.1016/j.aim.2020.107482.

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18

Paolini, Alessandro, e Iulian I. Simion. "On Refined Bruhat Decompositions and Endomorphism Algebras of Gelfand-Graev Representations". Algebras and Representation Theory 23, n. 4 (10 aprile 2019): 1243–63. http://dx.doi.org/10.1007/s10468-019-09885-5.

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19

Yamashita, Hiroshi. "On Whittaker vectors for generalized Gelfand-Graev representations of semisimple Lie groups". Proceedings of the Japan Academy, Series A, Mathematical Sciences 61, n. 7 (1985): 213–16. http://dx.doi.org/10.3792/pjaa.61.213.

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20

Yamashita, Hiroshi. "On Whittaker vectors for generalized Gelfand-Graev representations of semisimple Lie groups". Journal of Mathematics of Kyoto University 26, n. 2 (1986): 263–98. http://dx.doi.org/10.1215/kjm/1250520922.

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21

Curtis, C. W. "On the Gelfand-Graev Representations of a Reductive Group over a Finite Field". Journal of Algebra 157, n. 2 (giugno 1993): 517–33. http://dx.doi.org/10.1006/jabr.1993.1113.

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22

Yamashita, Hiroshi. "Finite multiplicity theorems for induced representations of semisimple Lie groups and their applications togeneralized Gelfand-Graev representations". Proceedings of the Japan Academy, Series A, Mathematical Sciences 63, n. 5 (1987): 153–56. http://dx.doi.org/10.3792/pjaa.63.153.

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23

Yamashita, Hiroshi. "Finite multiplicity theorems for induced representations of semisimpmle Lie groups II, -Applications to generalized Gelfand-Graev representations-". Journal of Mathematics of Kyoto University 28, n. 3 (1988): 383–444. http://dx.doi.org/10.1215/kjm/1250520400.

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24

Kawanaka, N. "Generalized Gelfand-Graev representations of exceptional simple algebraic groups over a finite field I". Inventiones Mathematicae 84, n. 3 (ottobre 1986): 575–616. http://dx.doi.org/10.1007/bf01388748.

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25

Rainbolt, Julianne G. "THE IRREDUCIBLE REPRESENTATIONS OF THE HECKE ALGEBRAS CONSTRUCTED FROM THE GELFAND-GRAEV REPRESENTATIONS OF GL(3, q) AND U(3, q)". Communications in Algebra 30, n. 9 (11 gennaio 2002): 4085–103. http://dx.doi.org/10.1081/agb-120013305.

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26

Rainbolt, Julianne G. "Notes on the norm map between the Hecke algebras of the Gelfand–Graev representations of GL(2,q2) and U(2,q)". Journal of Algebra 320, n. 9 (novembre 2008): 3493–511. http://dx.doi.org/10.1016/j.jalgebra.2008.07.025.

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27

Thiem, Nathaniel, e C. Ryan Vinroot. "Gelfand–Graev Characters of the Finite Unitary Groups". Electronic Journal of Combinatorics 16, n. 1 (30 novembre 2009). http://dx.doi.org/10.37236/235.

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Gelfand–Graev characters and their degenerate counterparts have an important role in the representation theory of finite groups of Lie type. Using a characteristic map to translate the character theory of the finite unitary groups into the language of symmetric functions, we study degenerate Gelfand–Graev characters of the finite unitary group from a combinatorial point of view. In particular, we give the values of Gelfand–Graev characters at arbitrary elements, recover the decomposition multiplicities of degenerate Gelfand–Graev characters in terms of tableau combinatorics, and conclude with some multiplicity consequences.
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28

Breeding-Allison, Jeffery, e Julianne Rainbolt. "The Gelfand-Graev Representation of GSp(4, 𝔽q)". Communications in Algebra, 7 ottobre 2016. http://dx.doi.org/10.1080/00927872.2016.1206341.

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29

Savin, Gordan, e Petar Bakic. "The Gelfand-Graev representation of classical groups in terms of Hecke algebras". Canadian Journal of Mathematics, 24 giugno 2022, 1–26. http://dx.doi.org/10.4153/s0008414x2200030x.

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30

Patel, Shiv, e Pooja Singla. "A multiplicity one theorem for groups of type 𝐴_{𝑛} over discrete valuation rings". Proceedings of the American Mathematical Society, 16 marzo 2022. http://dx.doi.org/10.1090/proc/15816.

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Let G \mathbf {G} be the General Linear or Special Linear group with entries from the finite quotients of the ring of integers of a non-archimedean local field and U \mathbf {U} be the subgroup of G \mathbf {G} consisting of upper triangular unipotent matrices. We prove that the induced representation Ind U G ⁡ ( θ ) \operatorname {Ind}^{\mathbf {G}}_{\mathbf {U}}(\theta ) of G \mathbf {G} obtained from a non-degenerate character θ \theta of U \mathbf {U} is multiplicity free for all ℓ ≥ 2. \ell \geq 2. This is analogous to the multiplicity one theorem regarding Gelfand-Graev representation for the finite Chevalley groups. We prove that for many cases the regular representations of G \mathbf {G} are characterized by the property that these are the constituents of the induced representation Ind U G ⁡ ( θ ) \operatorname {Ind}^{\mathbf {G}}_{\mathbf {U}}(\theta ) for some non-degenerate character θ \theta of U \mathbf {U} . We use this to prove that the restriction of a regular representation of General Linear groups to the Special Linear groups is multiplicity free and also obtain the corresponding branching rules in many cases.
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31

Andrews, Scott, e Nathaniel Thiem. "The generalized Gelfand–Graev characters of GLn(Fq)". Discrete Mathematics & Theoretical Computer Science DMTCS Proceedings, 28th... (22 aprile 2020). http://dx.doi.org/10.46298/dmtcs.6406.

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International audience Introduced by Kawanaka in order to find the unipotent representations of finite groups of Lie type, gener- alized Gelfand–Graev characters have remained somewhat mysterious. Even in the case of the finite general linear groups, the combinatorics of their decompositions has not been worked out. This paper re-interprets Kawanaka's def- inition in type A in a way that gives far more flexibility in computations. We use these alternate constructions to show how to obtain generalized Gelfand–Graev representations directly from the maximal unipotent subgroups. We also explicitly decompose the corresponding generalized Gelfand–Graev characters in terms of unipotent representations, thereby recovering the Kostka–Foulkes polynomials as multiplicities.
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32

GECK, MEINOLF. "GENERALISED GELFAND–GRAEV REPRESENTATIONS IN BAD CHARACTERISTIC ?" Transformation Groups, 22 maggio 2020. http://dx.doi.org/10.1007/s00031-020-09575-3.

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33

Taylor, Josephine. "The Lady in the Carriage: Trauma, Embodiment, and the Drive for Resolution". M/C Journal 15, n. 4 (14 agosto 2012). http://dx.doi.org/10.5204/mcj.521.

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Dream, 2008Go to visit a friend with vulvodynia who recently had a baby only to find that she is desolate. I realise the baby–a little boy–died. We go for a walk together. She has lost weight through the ordeal & actually looks on the edge of beauty for the first time. I feel like saying something to this effect–like she had a great loss but gained beauty as a result–but don’t think it would be appreciated. I know I shouldn’t stay too long &, sure enough, when we get back to hers, she indicates she needs for me to go soon. In her grief though, her body begins to spasm uncontrollably, describing the arc of the nineteenth-century hysteric. I start to gently massage her back & it brings her great relief as her body relaxes. I notice as I massage her, that she has beautiful gold and silver studs, flowers, filigree on different parts of her back. It describes a scene of immense beauty. I comment on it.In 2008, I was following a writing path dictated by my vulvodynia, or chronic vulval pain, and was exploring the possibility of my disorder being founded in trauma. The theory did not, in my case, hold up and I had decided to move on when serendipity intervened. Books ordered for different purposes arrived simultaneously and, as I dipped into the texts, I found startling correspondence between them. The books? Neurologist Jean-Martin Charcot’s lectures on hysteria, translated into English in 1889; psychiatrist W.H.R. Rivers’s explication of a biological theory of the neuroses published in 1922; and trauma neurologist Robert C. Scaer’s interpretation, in 2007, of the psychosomatic symptoms of his patients. The research grasped my intellect and imagination and maintained its grip until the ensuing chapter was done with me: my day life, papers and books skewed across tables; my night life, dreams surfeited with suffering and beauty, as I struggled with the possibility of any relationship between the two. Just as Rivers recognised that the shell-shock of World War I was not a physical injury as such but a trigger for and form of hysteria, so too, a few decades earlier, did Charcot insistently equate the railway brain/spine that resulted from railway accidents, with the hysteria of other of his patients, recognising that the precipitating incident constituted trauma that lodged in the body/mind of the victim (Clinical 221). More recently, Scaer notes that the motor vehicle accident (MVA) from which whiplash ensues is usually of insufficient force to logically cause bodily injury and, through this understanding, links whiplash and the railway brain/spine of the nineteenth century (25).In terms of comparative studies, most exciting for a researcher is the detail with which Charcot described patient after patient with hysteria in the Salpêtrière hospital, and elements of correspondence in symptomatology between these and Scaer’s patients, the case histories of which open most chapters of his book, titled appropriately, The Body Bears the Burden.Here are symptoms selected from a case study from each clinician:She subsequently developed headaches, neck pain, panic attacks, and full-blown post-traumatic stress disorder, along with significant cognitive problems [...] As her neck pain worsened and spread to her lower back, shoulders and arms, she noted increasing morning stiffness, and generalized pain and sensitivity to touch. With the development of interrupted, non-restorative sleep and chronic fatigue, she was ultimately diagnosed by a rheumatologist with fibromyalgia (Scaer 107).And:The patient suffers from a permanent headache of a constrictive character [...] All kinds of sound are painful to his ear, and he does his best to avoid them. It is impossible for him to fix his attention to any matter, or to devote himself to anything without speedily experiencing very great fatigue [...] He has insomnia and is frequently tormented by horrible dreams [...] Further, his memory appears to be considerably weakened (Charcot, Clinical 387).In the case of both patients, there was no significant physical injury, though both were left physically, as well as psychically, disabled. In the accidents that precipitated these symptoms, both were placed in positions of terrified helplessness as potential destruction bore down on them. In the case of Scaer’s patient, she froze in the driver’s seat at traffic lights as a large dump truck slowly reversed back on to her car, crushing the bonnet and engine compartment as it moved inexorably toward her. In the case of Charcot’s patient, he was dragging his barrow along the road when a laundryman’s van, pulled at “railway speed” by a careering horse, bore down on him, striking the wheel of his barrow (Clinical 375). It took some hours for the traumatised individuals of each incident to return to their senses.Scaer describes whiplash syndrome as “a diverse constellation of symptoms consisting of pain, neurologic symptoms, cognitive impairment, and emotional complaints” (xvii), and argues that the somatic or bodily expressions of the syndrome “may represent a universal constellation of symptoms attributable to any unresolved life-threatening experience” (143). Thus, as we look back through history, whiplash equals shell-shock equals railway brain equals the “swooning” and “vapours” of the eighteenth century (Shorter Chap. 1). All are precipitated by different causes, but all share the same outcome; diverse, debilitating symptoms affecting the body and mind, which have no reasonable physical explanation and which show no obvious organic cause. Human stress and trauma have always existed.In modern and historic studies of hysteria, much is made of the way in which the symptoms of hysterics have, over the centuries, mimicked “real” organic conditions (e.g. Shorter). Rivers discusses mimesis as a quality of the “gregarious” or herd instinct, noting that the enhanced suggestibility of such a state was utilised in military training. Here, preparation for combat focused on an unthinking obedience to duty and orders, and a loss of individual agency within the group: “The most successful training is one which attains such perfection of this responsiveness that each individual soldier not merely reacts at once to the expressed command of his superior, but is able to divine the nature of a command before it is given and acts as a member of the group immediately and effectively” (211–12). In the animal kingdom, the herd instinct manifests in behaviour that impacts the survival of prey and predator: schools of sardines move as one organism, seeking safety in numbers, while predatory sailfish act in silent concert to push the school into a tighter formation from which they can take orchestrated turns to feed.Unfortunately, the group mimesis created through a passive surrender of the individual ego to the herd, while providing a greater sense of security and chance of survival, also made World War I soldiers more vulnerable to the development of post-traumatic hysteria. At the Salpêtrière, Charcot described in meticulous detail the epileptic-like convulsions of hysteria major (la grande hystérie), which appeared to be an unwitting imitation of the seizures of epileptic inmates with whom hysteria patients were housed. Such convulsions included the infamous arc en circle, or backward-arched bodily semicircle, through which the individual’s body was thrust, up into the air, in an arc of distress only earthed by flexed feet and contorted neck (Veith 231). The suffering articulated in this powerful image stayed with me as I read, and percolated through my dreams.The three texts in which I remained transfixed had issued from different eras and used different language from each other, but all three contained similar and complementary insights. I found further correspondence between Charcot and Scaer in their understanding of the neurophysiology underlying hysteria/trauma. Though he did not have the technology to observe it, Charcot insisted that the symptoms of hysteria were the result of real changes in the nervous system. He distinguished between “organic” causes of disease, and the “functional” or “dynamic” causes of such disorders as hysteria and epilepsy: as he noted of the “hystero-traumatic paraplegia” of a patient, “it depends upon a dynamic lesion affecting the motor and sensory zones of the grey cortex of the brain which in a normal state preside over the functions of that limb” (Clinical 382). He proposed a potentially reversible “dynamic alteration” in the brain of the hysteric (Clinical 223–24). Compare Scaer: “Clinical syndromes previously categorized as ‘nonphysiological,’ ‘psychosomatic,’ or ‘functional’ may be based on demonstrable dynamic neurophysiological changes in the brain” (xx–xxi).Another link between the work of Charcot and Scaer is their insistence on the mind/body as a continuum, rather than separate entities. The perspicacity of the two researcher/clinicians forms bookends to a model separating mind from body that, in the wake of the popularisation and distortion of Freudian theory, characterised the twentieth-century. Said Charcot: “the physician must be a psychologist if he wants to interpret the most refined of cerebral functions, since psychology is nothing else but physiology of a part of the brain” (cited by Goetz 32). Says Scaer: “The distinction between the ‘psychological’ and physical pathological manifestations of traumatic stress, as suggested in the term ‘psychosomatic,’ needs to be discarded” (127). He proposes that, instead, we consider a mind/brain/body continuum which more accurately reflects, “the pathophysiological, neurobiological, endocrinological, and immunological changes induced by trauma” and the bodily manifestations of disease which follow (127).Charcot’s modernity is perhaps most evident in his understanding of equivalence between mind and brain, and his belief in what we now call “neuroplasticity”. Dealing with two patients with hysterical (traumatic) paralysis, Charcot recognised the value of friction, massage, and passive movements of the paralysed limb, not to build muscle strength, but to “revive” the “motor representation” in the brain as a necessary precursor to voluntary movement (Clinical 310). He noted the way in which, through repetition, movement strengthens. The parallel between Charcot’s insight, and recent research and practice which indicates that intense exercise for stroke victims assists the retrieval of motor programmes in the nervous system, in turn facilitating increased strength and movement, is quite astounding (Doidge Chap. 5).Scaer, like Rivers before him, understands the “freeze” or immobility response to threat as a very primitive or arcane level of the survival instinct. When neither fight nor flight will ensure an animal’s survival, it often manifests the freeze response, playing “dead”. After danger has passed, the animal might vibrate and shake, discharging the stored energy, physiologically “effecting” its defence or escape, and becoming fully functional again. Scaer describes this discharge process in animals as being “as imperceptible as a shudder, or as dramatic as a grand mal seizure” (19). The human, being an animal, also instinctually resorts to immobility when that is the reaction that will best ensure survival. As a result of this response, energy that would have been discharged in fighting or fleeing is bound up in the nervous system, along with accompanying terror, rage and helplessness. Unlike other animals that naturally discharge this energy when safe, humans often cognitively override the subtle but essential restorative behaviours that complete the full instinctual response, leaving them in a vicious cycle of fear and immobility and ultimately generating the symptoms of trauma.Scaer writes, “this apparent lack of discharge of autonomic energy after the occurrence of freezing [...] may represent a dangerous suppression of instinctual behavior, resulting in the imprinting of the traumatic experience in unconscious memory and arousal systems of the brain” (21). He proposes a persuasive model of “somatic dissociation” in which the body continues to manifest a threat to survival through impairment of the region of the body that perceived the sensory messages, and disability that reflects the incomplete motor defence (100). He writes of his patients in a chronic pain programme: “We invariably noticed that the patient’s unconscious posture reflected not only the pain, but also the experience of the traumatic event that produced the pain. The asymmetrical postural patterns, held in procedural memory, almost always reflect the body’s attempt to move away from the injury or threat that caused the injury” (84).Scaer’s concept of somatic dissociation, when applied to some of Charcot’s case studies, makes sense of their bodily symptoms. Charcot’s patient P— experiences no life threat, but a shock that involves grief and shame (Clinical 131–39). On a fox-hunting outing, he mistakes his friend’s dog for a fox, accidently shooting it dead. The friend is distraught, and P— consequently deeply distressed. He continues with the hunt, but later, when he raises his fire-arm to shoot a rabbit, collapses with a paralysis of the right side (he is right-handed), and then a loss of consciousness, with consequent confused recollection. Charcot’s lecture focuses on the “word-blindness” P— evidences, apparently associated with post-traumatic memory-deficits, but what is also arresting is the right-sided paralysis which lasts for some days, and the loss of vision on his right side. It is as if the act to shoot again is prevented by a body, shocked by its former action. The body parts affected hold meaning.In the case of the barrow man discussed earlier; although he has no lasting organic damage to his legs, nevertheless, his “feet remain literally fixed to the ground” (Clinical 378) when he is standing, perhaps reproducing the immobility with which he faced the rapidly looming van as it bore down on him. His paralysis speaks of his frozen helplessness, the trauma now locked in his body.In the case of the patient Ler—, aged around sixty, Charcot links her symptoms with a “series of frights” (Lectures 279): at eleven she was terrorised by a mad dog; at sixteen she was horrified by the sight of the corpse of a murdered woman; and, at the same age, she was threatened by robbers in a wood. During her violent hystero-epileptic attacks Ler— “hurls furious invectives against imaginary individuals, crying out, ‘villains! robbers! brigands! fire! fire! O, the dogs! I’m bitten!’” (Lectures 281). Here, the compilation of trauma is articulated through the body and the voice. Given that the extreme early childhood poverty and deprivation of Ler— were typical of hysterical patients at the Salpêtrière (Goetz 193), one might speculate that the hospital population of hysterics was composed of often severely traumatised women.The traumatised person is left with a constellation of symptoms familiar to anyone who has studied the history of hysteria. These comprise, but are not limited to, flashbacks, panic attacks, insomnia, depression, and unprovoked rage. The individual is also affected by physical symptoms that might include blindness or mutism, paralysis, spasms, skin anaesthesia, chronic fatigue, irritable bowel, migraines, or chronic pain. For trauma theorist Peter A. Levine, the key to healing lies in completing the original instinctual response; “trauma is part of a natural physiological process that simply has not been allowed to be completed” (155). The traumatised person stays stuck in or compulsively relives trauma in order to do just that. In 1885, Jean-Martin Charcot lectured at the Salpêtrière hospital in Paris, including among his case studies the patient he names Deb—. She resides more evocatively in my imagination as “the lady in the carriage”, a title drawn from Charcot’s description of her symptoms, and from the associated photographs which capture static moments of her frenzied and compulsive dance:Now look at this patient [...] In the first phase, rhythmical jerkings of the right arm, like the movements of hammering, occur [...] Then after this period there succeeds a period of tonic spasms, and of contortions of the arm and head, recalling partial epilepsy [...] Finally, measured movements of the head to the right and the left occur; rapid movements defying all interpretation, for I ask you, what do they correspond to in the region of physiological acts? At the same time the patient utters a cry, or rather a kind of plaintive wail, always the same [...] You see by this example that rhythmical chorea may be in certain cases a grave affection [affliction]. Not that it directly menaces life, but that it may persist over a very long period of time, and become a most distressing infirmity [...] The chorea has lasted for more than thirty years [...] The onset occurred at the age of thirty-six. About this time, when out driving in a carriage with her husband, she fell over a precipice with the horse and carriage. After the great fright which she had thus experienced she lost consciousness for three hours. This was followed by a convulsive seizure of hysteria major, by rigidity of the limbs of the right side, and cries like the barking of a dog (Clinical 193–95).I found this case study early in my reading of Charcot, but the lady in the carriage stayed with me as a trope of the relentless embodiment of trauma in its drive to be conclusively expressed, properly acknowledged, and potentially understood. Hence the persistent pain and distress of Scaer’s MVA patients; the patients treated by Rivers, with limbs and vocal-chords frozen in a never-ending moment of self-defence; the dramatic hysterical attacks of the impoverished patients in Charcot’s Salpêtrière; and the rhythmical chorea of the lady in the carriage, her involuntary jerky dance a physical re-enactment of her original trauma, when the carriage in which she was driving went over a precipice. Her helplessness in the event which precipitated her hysteria is a central factor in her continuing distress, her involuntary passivity removing her sense of agency and, like the soldier confined endlessly and powerlessly in the trenches waiting for inevitable terrifying action, rendering her unable to fight or flee.The fact that the lady in the carriage may be stuck in a traumatic incident experienced more than thirty years before attests to the way in which trauma insistently pushes to be resolved. Her re-enactment is literal, but Levine acknowledges the relevance of a “repetition compulsion” (181), expressed originally by Freud as the “compulsion to repeat” (19). This describes the often subtle way in which we continue to involve ourselves in situations that are replays of traumatic themes from childhood—symbolic re-enactments. Levine revitalises the idea however, by focusing on the interrupted instinctual response that calls for physiological resolution: “the drive to complete the freezing response remains active no matter how long it has been in place” (111).The knowledge a traumatised person seeks is, in trauma, literally locked in the body/mind. It rises up through dreams and throws itself aggressively at one in memories that are experienced as a terrifying present. It twists limbs in painful contractures and paralyzes the limb that was lifted in defence. The fear of turning to face this knowledge locks the individual in a recurring cycle of terror and immobility. At its end-point, s/he survives in the pathological limbo of Post-Traumatic Stress Disorder (PTSD), avoiding any arousal that might trigger all the physiological and emotional events of the original trauma. The original threat or trauma continues to exist in a perpetual present, with the individual unable to relegate it to the past as a bearable memory.It is possible to interpret such suffering in many ways. One might, for instance, focus on the pathology of an apparent system malfunction, which keeps the body/mind inefficiently glued to an unsolvable past. I choose to emphasise here, however, the creativity and persistence of the human body/mind in its drive to resolve the response to trauma, recover equilibrium and face effectively the recurrent challenges of life. As well as physical symptoms which exact attention, this drive or instinct might include the prompting of dreams and the meaningful coincidences we notice as we open our eyes to them, all of which can lead us down previously unconsidered paths. Does the body/mind only continue to malfunction due to our inability to correctly decipher its language? In relation to trauma, the body/mind bears the burden, but it might also hold the key to recovery.References Charcot, Jean-Martin. Lectures on the Diseases of the Nervous System. Trans. George Sigerson. London: The New Sydenham Society, 1877.---. Clinical Lectures on Diseases of the Nervous System: Volume 3. Trans. Thomas Savill. London: The New Sydenham Society, 1889.Doidge, Norman. The Brain That Changes Itself: Stories of Personal Triumph from the Frontiers of Brain Science. Melbourne: Scribe, 2008.Freud, Sigmund. “Beyond the Pleasure Principle.” The Standard Edition of the Complete Psychological Works of Sigmund Freud. Ed. and Trans. James Strachey. London: Hogarth Press, 1955. 7–64.Goetz, Christopher G, Michel Bonduelle, and Toby Gelfand. Charcot: Constructing Neurology. New York: Oxford University Press, 1995.Levine, Peter A. Waking the Tiger: Healing Trauma: The Innate Capacity to Transform Overwhelming Experiences. Berkeley, CA: North Atlantic Books, 1997.Rivers, W. H. R. Instinct and the Unconscious: A Contribution to a Biological Theory of the Psycho-Neuroses. 2nd ed. Cambridge: Cambridge University Press, 1922.Scaer, Robert C. The Body Bears the Burden: Trauma, Dissociation, and Disease. 2nd ed. New York: Haworth Press, 2007.Shorter, Edward. From Paralysis to Fatigue: A History of Psychosomatic Illness in the Modern Era. New York: Free Press, 1992.Veith, Ilza. Hysteria: The History of a Disease. Chicago: University of Chicago Press, 1965.
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