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Relevant bibliographies by topics / Gelfand–Graev representation

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Academic literature on the topic 'Gelfand–Graev representation'

Author: Grafiati

Published: 16 November 2022

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Journal articles on the topic "Gelfand–Graev representation"

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

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