A q-Analogue of Derivations on the Tensor Algebra and the q-Schur-Weyl Duality

被引：0

作者：

Itoh, Minoru ^{[1
]}

机构：

[1] Kagoshima Univ, Dept Math & Comp Sci, Fac Sci, Kagoshima 8900065, Japan

来源：

LETTERS IN MATHEMATICAL PHYSICS | 2015年 / 105卷 / 10期

关键词：

Tensor algebra; Weyl algebra; Clifford algebra; quantum enveloping algebra; Iwahori-Hecke algebra; Schur-Weyl duality;

D O I：

10.1007/s11005-015-0793-7

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

This paper presents a q-analogue of an extension of the tensor algebra given by the same author. This new algebra naturally contains the ordinary tensor algebra and the Iwahori-Hecke algebra type A of infinite degree. Namely, this algebra can be regarded as a natural mix of these two algebras. Moreover, we can consider natural "derivations" on this algebra. Using these derivations, we can easily prove the q-Schur-Weyl duality (the duality between the quantum enveloping algebra of the general linear Lie algebra and the Iwahori-Hecke algebra of type A).

引用

页码：1467 / 1477

页数：11

共 8 条

[1]

Goodman R., 2003, REPRESENTATIONS INVA

[2] ON THE SEMISIMPLICITY OF HECKE ALGEBRAS [J].