Готові списки джерел за темами / Représentation de Gelfand–Graev

Добірка наукової літератури з теми "Représentation de Gelfand–Graev"

Автор: Grafiati
Опубліковано: 16 листопада 2022
Оновлено: 16 грудня 2022

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Зміст

  1. Статті в журналах
  2. Дисертації
  3. Частини книг

Статті в журналах з теми "Représentation de Gelfand–Graev":

1

Sorlin, Karine. "Représentations de Gelfand–Graev pour les groupes réductifs non connexes." Comptes Rendus Mathematique 334, no. 3 (February 2002): 179–84. http://dx.doi.org/10.1016/s1631-073x(02)02239-2.

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2

Sorlin, Karine. "Éléments réguliers et représentations de Gelfand-Graev des groupes réductifs non connexes." Bulletin de la Société mathématique de France 132, no. 2 (2004): 157–99. http://dx.doi.org/10.24033/bsmf.2463.

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3

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 Lusztig’s work in characteristic 0 [Lu2].
4

Mishra, Manish, and Basudev Pattanayak. "Principal series component of Gelfand-Graev representation." Proceedings of the American Mathematical Society 149, no. 11 (August 5, 2021): 4955–62. http://dx.doi.org/10.1090/proc/15642.

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5

Geck, Meinolf. "Character Sheaves and Generalized Gelfand-Graev Characters." Proceedings of the London Mathematical Society 78, no. 1 (January 1999): 139–66. http://dx.doi.org/10.1112/s0024611599001641.

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6

TAYLOR, JAY. "GENERALIZED GELFAND–GRAEV REPRESENTATIONS IN SMALL CHARACTERISTICS." Nagoya Mathematical Journal 224, no. 1 (September 9, 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 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 $\mathbf{G}$.
7

Letellier, Emmanuel. "Deligne–Lusztig restriction of Gelfand–Graev characters." Journal of Algebra 294, no. 1 (December 2005): 239–54. http://dx.doi.org/10.1016/j.jalgebra.2005.05.031.

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8

Chan, Kei Yuen, and Gordan Savin. "Iwahori component of the Gelfand–Graev representation." Mathematische Zeitschrift 288, no. 1-2 (March 23, 2017): 125–33. http://dx.doi.org/10.1007/s00209-017-1882-3.

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9

RAINBOLT, JULIANNE G. "WEYL GROUPS AND BASIS ELEMENTS OF HECKE ALGEBRAS OF GELFAND–GRAEV REPRESENTATIONS." Journal of Algebra and Its Applications 10, no. 05 (October 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).
10

Dudas, Olivier. "Deligne-Lusztig restriction of a Gelfand-Graev module." Annales scientifiques de l'École normale supérieure 42, no. 4 (2009): 653–74. http://dx.doi.org/10.24033/asens.2105.

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Статті в журналах

Дисертації з теми "Représentation de Gelfand–Graev":

1

Sorlin, Karine. "Représentations de Gelfand-Graev et correspondance de Springer dans les groupes réductifs non connexes." Amiens, 2001. http://www.theses.fr/2001AMIE0009.

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2

Li, Tzu-Jan. "On the endomorphism algebra of Gelfand–Graev representations and the unipotent ℓ-block of p-adic GL2 with ℓ ≠ p". Thesis, Sorbonne université, 2022. http://www.theses.fr/2022SORUS271.

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Inspiré par la conjecture de Langlands locale en familles de Dat, Helm, Kurinczuk et Moss, pour un groupe réductif connexe G défini sur F_q, nous étudions les relations des trois anneaux suivants : (i) le Z-modèle E_G des algèbres d’endomorphismes des représentations de Gelfand–Graev de G(F_q) ; (ii) l’anneau de Grothendieck K_{G*} de la catégorie des représentations de G*(F_q) de dimension finie sur F_q, avec G* le dual de Deligne–Lusztig de G ; (iii) l’anneau des fonctions B_{G^vee} du Z-schéma (T^vee // W)^{F^vee}, avec G^vee le dual de Langlands (défini et déployé sur Z) de G. Nous démontrons que Z[1/pM]E_G simeq Z[1/pM]K_{G*} comme Z[1/pM]-algèbres avec p = char(F_q) et M le produit des nombres premiers mauvais pour G, et que K_{G*} simeq B_{G^vee} comme anneaux lorsque le groupe dérivé de G^vee est simplement connexe. Profitant de ces résultats, nous donnons ensuite une description explicite du l-bloc unipotent de GL_2 p-adique avec l différent de p. Les matériaux de ce travail, sauf § 4, proviennent principalement de mon article [Li2] et de mon autre article [LiSh] en collaboration avec J. Shotton
Inspired by the conjecture of local Langlands in families of Dat, Helm, Kurinczuk and Moss, for a connected reductive group G defined over F_q, we study the relations of the following three rings: (i) the Z-model E_G of endomorphism algebras of Gelfand–Graev representations of G(F_q); (ii) the Grothendieck ring K_{G*} of the category of representations of G*(F_q) of finite dimension over F_q, with G* the Deligne–Lusztig dual of G; (iii) the ring of functions B_{G^vee} of (T^vee // W)^{F^vee}, with G^vee the Langlands dual (defined and split over Z) of G. We show that Z[1/pM]E_G simeq Z[1/pM]K_{G*} as Z[1/pM]-algebras with p = char(F_q) and M the product of bad primes for G, and that K_{G*} simeq B_{G^vee} as rings when the derived subgroup of G^vee is simply-connected. Benefiting from these results, we then give an explicit description of the unipotent l-block of p-adic GL_2 with l different from p. The material of this work, except for § 4, mainly originates from my article [Li2] and from my other article [LiSh] in collaboration with J. Shotton
3

Dudas, Olivier. "Géométrie des variétés de Deligne-Lusztig, décompositions, cohomologie modulo \ell et représentations modulaires." Phd thesis, Université de Franche-Comté, 2010. http://tel.archives-ouvertes.fr/tel-00492848.

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Анотація:
Cette thèse porte sur la construction et l'étude des représentations modulaires des groupes réductifs finis. Comme dans le cas ordinaire, l'accent est mis sur les constructions de nature géométrique, obtenues à partir de la cohomologie des variétés de Deligne-Lusztig. On commence par introduire des méthodes de décomposition du type Deodhar, permettant de déterminer en toute généralité la présence d'une classe particulière de représentations, les modules de Gelfand-Graev, ainsi que certaines de leurs versions généralisées. Des résultats plus précis sont ensuite démontrés pour des variétés associées à certains éléments réguliers de petite longueur. Le cas des éléments de Coxeter tient une place importante dans ce mémoire : pour ces éléments, on détermine un représentant explicite du complexe de cohomologie, aboutissant à une preuve de la version géométrique de la conjecture de Broué pour certains nombres premiers. On en déduit aussi la forme de l'arbre de Brauer du bloc principal dans ce cas, ce qui résout une conjecture de Hiss, Lübeck et Malle. Ces deux résultats sont conditionnés par une hypothèse assurant l'absence de torsion dans la cohomologie, dont on montre qu'elle est satisfaite pour de nombreux groupes classiques et exceptionnels.
4

Khoury, Michael John Jr. "Multiplicity One Results and Explicit Formulas for Quasi-Split p-adic Unitary Groups." The Ohio State University, 2008. http://rave.ohiolink.edu/etdc/view?acc_num=osu1218567821.

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5

Taylor, Jonathan. "On Unipotent Supports of Reductive Groups With a Disconnected Centre." Phd thesis, University of Aberdeen, 2012. http://tel.archives-ouvertes.fr/tel-00709051.

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Let $\mathbf{G}$ be a connected reductive algebraic group defined over an algebraic closure of the finite field of prime order $p>0$, which we assume to be good for $\mathbf{G}$. We denote by $F : \mathbf{G} \to \mathbf{G}$ a Frobenius endomorphism of $\mathbf{G}$ and by $G$ the corresponding $\mathbb{F}_q$-rational structure. If $\operatorname{Irr}(G)$ denotes the set of ordinary irreducible characters of $G$ then by work of Lusztig and Geck we have a well defined map $\Phi_{\mathbf{G}} : \operatorname{Irr}(G) \to \{F\text{-stable unipotent conjugacy classes of }\mathbf{G}\}$ where $\Phi_{\mathbf{G}}(\chi)$ is the unipotent support of $\chi$.

Lusztig has given a classification of the irreducible characters of $G$ and obtained their degrees. In particular he has shown that for each $\chi \in \operatorname{Irr}(G)$ there exists an integer $n_{\chi}$ such that $n_{\chi}\cdot\chi(1)$ is a monic polynomial in $q$. Given a unipotent class $\mathcal{O}$ of $\mathbf{G}$ with representative $u \in \mathbf{G}$ we may define $A_{\mathbf{G}}(u)$ to be the finite quotient group $C_{\mathbf{G}}(u)/C_{\mathbf{G}}(u)^{\circ}$. If the centre $Z(\mathbf{G})$ is connected and $\mathbf{G}/Z(\mathbf{G})$ is simple then Lusztig and H\'zard have independently shown that for each $F$-stable unipotent class $\mathcal$ of $\mathbf$ there exists $\chi \in \operatorname(G)$ such that $\Phi_(\chi)=\mathcal$ and $n_ = |A_(u)|$, (in particular the map $\Phi_$ is surjective).

The main result of this thesis extends this result to the case where $\mathbf$ is any simple algebraic group, (hence removing the assumption that $Z(\mathbf)$ is connected). In particular if $\mathbf$ is simple we show that for each $F$-stable unipotent class $\mathcal$ of $\mathbf$ there exists $\chi \in \operatorname(G)$ such that $\Phi_(\chi) = \mathcal$ and $n_ = |A_(u)^F|$ where $u \in \mathcal^F$ is a well-chosen representative. We then apply this result to prove, (for most simple groups), a conjecture of Kawanaka's on generalised Gelfand--Graev representations (GGGRs). Namely that the GGGRs of $G$ form a $\mathbf{Z}$-basis for the $\mathbf{Z}$-module of all unipotently supported class functions of $G$. Finally we obtain an expression for a certain fourth root of unity associated to GGGRs in the case where $\mathbf{G}$ is a symplectic or special orthogonal group.

6

Hezard, David. "Sur le support unipotent des faisceaux-caractères." Phd thesis, Université Claude Bernard - Lyon I, 2004. http://tel.archives-ouvertes.fr/tel-00012071.

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Soit G un groupe algébrique réductif connexe de centre connexe défini sur un corps fini de caractéristique p>0. On munit cette structure d'un endomorphisme de Frobenius F et l'on note G^F l'ensemble des points de G fixes pour l'action de F : G^F est un groupe fini. On suppose que la caractéristique p est bonne pour G.

On définit alors une application Phi_G de l'ensemble des classes de conjugaison spéciales de G^* dans l'ensemble des classes unipotentes de G. Cette application décrit le support unipotent des différentes classes de faisceaux-caractères définis sur G.

Parallèlement à cela, via la correspondance de Springer, on définit différents invariants, dont les d-invariants, pour les caractères d'un groupe de Weyl W. Nous avons étudié le lien entre l'induction de caractères spéciaux de certains sous groupes de W et les d-invariants. A l'aide de ceci, on démontre que Phi_G, restreinte à certaines classes spéciales particulières de G^* est surjective. On a montré que la stabilité vis-à-vis du Frobenius pouvait être introduite dans ce résultat.

On en déduit deux résultats. Le premier est un lien étroit entre les restrictions aux éléments unipotents de faisceaux-caractères de certaines classes et différents systèmes locaux irréductibles et G-équivariants sur les classes unipotentes de G.

Le second est une preuve d'une conjecture de Kawanaka sur les caractères de Gelfand-Graev généralisés de G : ils forment une base du Z-module des caractères virtuels de G^F à support unipotent.
7

Matos, Pedro Alexandre Correia de. "O carácter de Gelfand-Graev e generalizações." Master's thesis, 2015. http://hdl.handle.net/10451/20291.

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Tese de mestrado em Matemática, apresentada à Universidade de Lisboa, através da Faculdade de Ciências, 2015
O principal objectivo desta dissertação é o de apresentar a construção de uma família de caracteres do grupo GL(n; q), que generalize de algum modo a construção do seu carácter de Gelfand-Graev. A nossa construção é essencialmente uma adaptação da construção proposta por N. Kawanaka no âmbito dos grupos algébricos redutivos conexos. Passando ao fecho algébrico K, os nossos argumentos baseiam-se sobretudo no uso de informação respeitante ao modo como GL(n;K) actua na sua álgebra de Lie gl(n;K), vendo GL(n; q) como o conjunto dos pontos fixos em GL(n;K) por um certo morfismo. O tratamento já conhecido destas questões costuma impor fortes restrições sobre a característica do corpo base. No entanto, o nosso trabalho mostra como podemos "aliviar" esta restrição quando trabalhamos no grupo GL(n;K). O presente trabalho é de carácter expositório, embora algumas observações permitam ligar o nosso material a outros estudos recentes, em particular no âmbito da teoria de supercaracteres do grupo unitriangular finito.
The main goal of this master thesis is that of constructing a family of characters from the group GL(n; q), such that this construction generalizes, in a certain way, the construction of the more familiar Gelfand-Graev character. Our treatment amounts to an adaptation of the original construction due to N. Kawanaka for connected reductive linear algebraic groups. By taking the algebraic closure of our finite base field, we look at the action of the algebraic group GL(n;K) on its Lie algebra gl(n;K), where GL(n; q) is the set of fixed points in GL(n;K) by a certain morphism. A forceful restriction on the characteristic of the base field arises in the general treatment of these questions, but our work shows us that this restriction can be further improved when working with GL(n;K). We should refer that our work is mainly expository, but the way in which we treat this material can somehow be linked to further research in other fields, such as in supercharacter theory of the finite unitriangular group.

Частини книг з теми "Représentation de Gelfand–Graev":

1

Curtis, Charles W. "On the Endomorphism Algebras of Gelfand-Graev Representations." In Finite Dimensional Algebras and Related Topics, 27–35. Dordrecht: Springer Netherlands, 1994. http://dx.doi.org/10.1007/978-94-017-1556-0_2.

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2

Curtis, Charles W., and Toshiaki Shoji. "A Norm Map for Endomorphism Algebras of Gelfand-Graev Representations." In Finite Reductive Groups: Related Structures and Representations, 185–94. Boston, MA: Birkhäuser Boston, 1997. http://dx.doi.org/10.1007/978-1-4612-4124-9_7.

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3

"Regular elements; Gelfand-Graev representations." In Representations of Finite Groups of Lie Type, 119–42. Cambridge University Press, 1991. http://dx.doi.org/10.1017/cbo9781139172417.016.

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4

"Regular Elements; Gelfand–Graev Representations; Regular and Semi-Simple Characters." In Representations of Finite Groups of Lie Type, 196–224. Cambridge University Press, 2020. http://dx.doi.org/10.1017/9781108673655.014.

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5

"Coefficients of Gelfand-Graev Type, of Fourier-Jacobi Type, and Descent." In The Descent Map from Automorphic Representations of GL(n) to Classical Groups, 41–63. WORLD SCIENTIFIC, 2011. http://dx.doi.org/10.1142/9789814304993_0003.

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6

"Jacquet modules corresponding to Gelfand - Graev characters of parabolically induced representations." In The Descent Map from Automorphic Representations of GL(n) to Classical Groups, 81–120. WORLD SCIENTIFIC, 2011. http://dx.doi.org/10.1142/9789814304993_0005.

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7

Yamashita, Hiroshi. "Multiplicity One Theorems for Generalized Gelfand-Graev Representations of Semisimple Lie Groups and Whittaker Models for the Discrete Series." In Representations of Lie Groups, Kyoto, Hiroshima, 1986, 31–121. Elsevier, 1988. http://dx.doi.org/10.1016/b978-0-12-525100-6.50007-2.

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