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Journal articles on the topic 'Gelfand–Graev representation'

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Published: 16 November 2022

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1

Mishra, Manish, and Basudev Pattanayak. "Principal series component of Gelfand-Graev representation." Proceedings of the American Mathematical Society 149, no. 11 (2021): 4955–62. http://dx.doi.org/10.1090/proc/15642.

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2

Chan, Kei Yuen, and Gordan Savin. "Iwahori component of the Gelfand–Graev representation." Mathematische Zeitschrift 288, no. 1-2 (2017): 125–33. http://dx.doi.org/10.1007/s00209-017-1882-3.

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3

Breeding-Allison, Jeffery, та Julianne Rainbolt. "The Gelfand–Graev representation of GSp(4,𝔽q)". Communications in Algebra 47, № 2 (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, no. 2 (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, no. 1 (2016): 93–167. http://dx.doi.org/10.1017/nmj.2016.33.

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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 o

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6

Curtis, Charles W., and Ken-ichi Shinoda. "Unitary Kloosterman Sums and the Gelfand–Graev Representation of GL2." Journal of Algebra 216, no. 2 (1999): 431–47. http://dx.doi.org/10.1006/jabr.1998.7807.

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7

Kochubei, Anatoly N., and Yuri Kondratiev. "Representations of the infinite-dimensional p-adic affine group." Infinite Dimensional Analysis, Quantum Probability and Related Topics 23, no. 01 (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, no. 02 (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 f

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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, no. 1 (2020): 109–19. http://dx.doi.org/10.2140/pjm.2020.307.109.

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10

Bonnafé, Cédric, and 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 Luszt

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11

SHINODA, KENICHI, and ILKNUR TULUNAY. "REPRESENTATIONS OF THE HECKE ALGEBRA FOR GL4(q)." Journal of Algebra and Its Applications 04, no. 06 (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, no. 10 (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, no. 5 (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, no. 1 (1998): 44–71. http://dx.doi.org/10.1006/jabr.1997.7250.

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15

Bonnafé, Cédric, and Radha Kessar. "On the endomorphism algebras of modular Gelfand–Graev representations." Journal of Algebra 320, no. 7 (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, no. 05 (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

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17

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

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18

Paolini, Alessandro, and Iulian I. Simion. "On Refined Bruhat Decompositions and Endomorphism Algebras of Gelfand-Graev Representations." Algebras and Representation Theory 23, no. 4 (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, no. 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, no. 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, no. 2 (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, no. 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, no. 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, no. 3 (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, no. 9 (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, no. 9 (2008): 3493–511. http://dx.doi.org/10.1016/j.jalgebra.2008.07.025.

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27

Thiem, Nathaniel, and C. Ryan Vinroot. "Gelfand–Graev Characters of the Finite Unitary Groups." Electronic Journal of Combinatorics 16, no. 1 (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

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28

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

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29

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

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30

Patel, Shiv, та Pooja Singla. "A multiplicity one theorem for groups of type 𝐴_{𝑛} over discrete valuation rings". Proceedings of the American Mathematical Society, 16 березня 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 fo

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31

Andrews, Scott, and Nathaniel Thiem. "The generalized Gelfand–Graev characters of GLn(Fq)." Discrete Mathematics & Theoretical Computer Science DMTCS Proceedings, 28th... (April 22, 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 explicitl

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32

GECK, MEINOLF. "GENERALISED GELFAND–GRAEV REPRESENTATIONS IN BAD CHARACTERISTIC ?" Transformation Groups, May 22, 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, no. 4 (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, d

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