Dirac Cohomology and \(\Theta \)-correspondence for Complex Dual Pairs

IF 0.5 4区数学 Q3 MATHEMATICS

Algebras and Representation Theory Pub Date : 2025-02-08 DOI:10.1007/s10468-025-10319-8

S. Afentoulidis-Almpanis, G. Liu, S. Mehdi

引用次数: 0

Abstract

We study the behavior of Dirac cohomology under Howe’s \(\Theta \)-correspondence in the case of complex reductive dual pairs. More precisely, if \((G_1,G_2)\) is a complex reductive dual pair with \(G_1\) and \(G_2\) viewed as real groups, we describe those Harish-Chandra modules \(\pi _1\) of \(G_1\) with nonzero Dirac cohomology whose \(\Theta \)-liftings \(\Theta (\pi _1)\) still have nonzero Dirac cohomology. In this case, we compute explicitly the Dirac cohomology of \(\Theta (\pi _1)\).

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来源期刊

Algebras and Representation Theory 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Algebras and Representation Theory features carefully refereed papers relating, in its broadest sense, to the structure and representation theory of algebras, including Lie algebras and superalgebras, rings of differential operators, group rings and algebras, C*-algebras and Hopf algebras, with particular emphasis on quantum groups. The journal contains high level, significant and original research papers, as well as expository survey papers written by specialists who present the state-of-the-art of well-defined subjects or subdomains. Occasionally, special issues on specific subjects are published as well, the latter allowing specialists and non-specialists to quickly get acquainted with new developments and topics within the field of rings, algebras and their applications.