Compact Schur-Weyl duality and the Type B/C VW-algebra

被引：1

作者：

Calvert, Kieran ^{[1
]}

机构：

[1] Univ Manchester, Dept Math, Manchester, England

来源：

ADVANCES IN MATHEMATICS | 2022年 / 407卷

关键词：

Schur-Weylduality; Liealgebras; Braueralgebras; DIRAC COHOMOLOGY; BRAUER ALGEBRAS; UNITARY REPRESENTATIONS; HECKE ALGEBRAS; AFFINE;

D O I：

10.1016/j.aim.2022.108575

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study a compact analogue of Schur-Weyl duality for real orthogonal and symplectic groups. We analyse the functors F-mu,F-k defined in [12], and introduce a new algebra B-k(0). This algebra's finite dimensional modules are naturally a co-domain for the functors F-mu,F-k. With this new insight, we prove that principle series modules map to principles series modules of graded Hecke algebras and these functors preserve Langlands quotients and unitarity of Harish-Chandra modules. (C) 2022 The Author(s). Published by Elsevier Inc.

引用

页数：41

共 31 条

[1]

[Anonymous], 1989, Journal of the American Mathematical Society

[2] Duality between ζιn(C) and the degenerate affine Hecke algebra [J].