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

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