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.
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页码：1433 / 1441
页数：9
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