On Refined Bruhat Decompositions and Endomorphism Algebras of Gelfand-Graev Representations

被引：0

作者：

Paolini, Alessandro ^{[1
]}

Simion, Iulian I. ^{[2
]}

机构：

[1] Tech Univ Kaiserslautern, Fachbereich Math, Postfach 3049, D-67653 Kaiserslautern, Germany

[2] Babes Bolyai Univ, Dept Math, Math 9, Ploiesti 23-25, Cluj Napoca, Romania

来源：

ALGEBRAS AND REPRESENTATION THEORY | 2020年 / 23卷 / 04期

关键词：

Gelfand-Graev representations; Kloosterman sums; Refined Bruhat cells; STRUCTURE CONSTANTS; HECKE ALGEBRAS; CHARACTERS;

D O I：

10.1007/s10468-019-09885-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

LetGbe a finite reductive group defined over F-q, with q a power of a primep. Motivated by a problem recently posed by C. Curtis, we first develop an algorithm to express each element ofGinto a canonical form in terms of a refinement of a Bruhat decomposition, and we then use the output of the algorithm to explicitly determine the structure constants with respect to a standard basis of the endomorphism algebra of a Gelfand-Graev representation of G when G= PGL(3)(q) for an arbitrary primep, and when G = SO5(q) forpodd.

引用

页码：1243 / 1263

页数：21

共 22 条

[1]

[Anonymous], 1991, LONDON MATH SOC STUD

[2]

[Anonymous], 1994, ENCY MATH ITS APPL

[3]

[Anonymous], 1998, MATH SURVEYS MONOGRA, DOI DOI 10.1090/SURV/040.3

[4]

[Anonymous], 1975, OSAKA J MATH

[5] On the endomorphism algebras of modular Gelfand-Graev representations [J].

Bonnafe, Cedric ;

Kessar, Radha .

JOURNAL OF ALGEBRA, 2008, 320 (07) :2847-2870

[6]

Carter RW, 1985, PURE APPL MATH, V44, P544

[7]

Carter RW, 1989, SIMPLE GROUPS LIE TY, P331

[8] DECOMPOSITION OF GELFAND-GRAEV CHARACTERS OF GL3(Q) [J].

CHANG, B .

COMMUNICATIONS IN ALGEBRA, 1976, 4 (04) :375-401

[9]

Curtis, 1990, METHODS REPRESENTATI, VI

[10] NOTES ON THE STRUCTURE CONSTANTS OF HECKE ALGEBRAS OF INDUCED REPRESENTATIONS OF FINITE CHEVALLEY GROUPS [J].

Curtis, Charles W. .

PACIFIC JOURNAL OF MATHEMATICS, 2015, 279 (1-2) :181-202

← 1 2 3 →