On representations of Hecke algebras

被引：13

作者：

Isaev, AP ^{[1
]}

Ogievetsky, O

机构：

[1] Bogoliubov Lab Theoret Phys, Joint Nucl Res Inst, Dubna 141980, Moscow Region, Russia

[2] Ctr Theoret Phys, F-13288 Marseille, France

来源：

CZECHOSLOVAK JOURNAL OF PHYSICS | 2005年 / 55卷 / 11期

基金：

俄罗斯基础研究基金会;

关键词：

representation theory; symmetric groups; Hecke algebras; Jucys-Murphy elements; maximal commutative subalgebra; Young diagram; Young graph; q-dimension;

D O I：

10.1007/s10582-006-0022-9

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

In this report we review some facts about representation theory of Hecke algebras. For Hecke algebras we adapt the approach of A. Okounkov and A. Vershik [Selecta Math., New Ser., 2 (1996) 581], which was developed for the representation theory of symmetric groups. We justify explicit construction of idempotents for Hecke algebras in terms of Jucys-Murphy elements. Ocneanu's traces for these idempotents (which can be interpreted as q-dimensions of corresponding irreducible representations of quantum linear groups) are presented.

引用

页码：1433 / 1441

页数：9

共 50 条

[31] Local and global methods in representations of Hecke algebras
Jie Du
Brian J. Parshall
Leonard L. Scott
Science China Mathematics, 2018, 61 : 207 - 226
[32] Finite Weil representations and associated Hecke algebras
Nebe, Gabriele
JOURNAL OF NUMBER THEORY, 2009, 129 (03) : 588 - 603
[33] Local and global methods in representations of Hecke algebras
Jie Du
Brian J.Parshall
Leonard L.Scott
Science China(Mathematics), 2018, 61 (02) : 207 - 226
[34] HECKE AND INDUCED ALGEBRAS OF CUSPIDAL REPRESENTATIONS, FOR GL(N)
WALDSPURGER, JL
JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 1986, 370 : 127 - 191
[35] COCENTERS AND REPRESENTATIONS OF PRO-p HECKE ALGEBRAS
He, Xuhua
Nie, Sian
REPRESENTATION THEORY, 2017, 21 : 82 - 105
[36] Irreducibility of perfect representations of double affine Hecke algebras
Cherednik, I
STUDIES IN LIE THEORY: DEDICATED TO A. JOSEPH ON HIS SIXTIETH BIRTHDAY, 2006, 243 : 79 - 95
[37] EQUIVARIANT K-THEORY AND REPRESENTATIONS OF HECKE ALGEBRAS
LUSZTIG, G
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1985, 94 (02) : 337 - 342
[38] Images of Galois representations in mod p Hecke algebras
Amoros, Laia
INTERNATIONAL JOURNAL OF NUMBER THEORY, 2021, 17 (05) : 1265 - 1285
[39] Strata Hasse invariants, Hecke algebras and Galois representations
Goldring, Wushi
Koskivirta, Jean-Stefan
INVENTIONES MATHEMATICAE, 2019, 217 (03) : 887 - 984
[40] Cyclic generators for irreducible representations of affine Hecke algebras
Guizzi, Valentina
Nazarov, Maxim
Papi, Paolo
JOURNAL OF COMBINATORIAL THEORY SERIES A, 2010, 117 (06) : 683 - 703

← 1 2 3 4 5 →