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.
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页数：41
相关论文
共 31 条
[21]   DIRAC COHOMOLOGY OF SOME HARISH-CHANDRA MODULES [J].
Huang, Jing-Song ;
Kang, Yi-Fang ;
Pandzic, Pavle .
TRANSFORMATION GROUPS, 2009, 14 (01) :163-173
[22]   Dirac cohomology, unitary representations and a proof of a conjecture of Vogan [J].
Huang, JS ;
Pandzic, P .
JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, 2002, 15 (01) :185-202
[23]   ON SOME TYPES OF TOPOLOGICAL GROUPS [J].
IWASAWA, K .
ANNALS OF MATHEMATICS, 1949, 50 (03) :507-558
[24]  
Knapp A.W., 2013, LIE GROUPS INTRO, V140
[25]  
Kriloff C., 2002, Represent. Theory, V6, P31, DOI [10.1090/S1088-4165-02-00160-7, DOI 10.1090/S1088-4165-02-00160-7]
[26]  
Pantano A., 2010, REPRESENT THEOR, P201
[27]   The integrity of the primitive representations of a closed continuous group [J].
Peter, F ;
Weyl, H .
MATHEMATISCHE ANNALEN, 1927, 97 :737-755
[28]   Classification of graded Hecke algebras for complex reflection groups [J].
Ram, A ;
Shepler, AV .
COMMENTARII MATHEMATICI HELVETICI, 2003, 78 (02) :308-334
[29]  
Vogan D., 2015, LINEAR PROJECTIVE RE
[30]  
Vogan D., 1981, Representations of Real Reductive Groups
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