Identification of simple representations for affine q-Schur algebras

JOURNAL OF ALGEBRA

卷:373

Article

Deng, Bangming¹  Du, Jie² 

[1] Beijing Normal Univ, Sch Math Sci, Beijing 100875, Peoples R China

[2] Univ New S Wales, Sch Math & Stat, Sydney, NSW 2052, Australia

关键词: Affine q-Schur algebra;    Quantum loop algebra;    Affine Hecke algebra;    Simple representation;   

DOI  :  10.1016/j.jalgebra.2012.10.013

来源: Elsevier

【 摘 要 】

We define an explicit action of the quantum loop algebra U-q((g) over capI(n)) on the tensor space and show that these actions are compatible with the natural embedding U-q((g) over capI(n)) hooked right arrow U-q((g) over capI(n+1)). As an application, we identify simple representations of affine q-Schur algebras S-Delta (n, r)(C) arising from simple polynomial representations of U-q((g) over capI(n)) (Frenkel and Mukhin, 2002) [11] with those arising from simple modules of the affine Hecke algebra H-Delta(r)(C) of type A (Rogawski, 1985) [26]. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free