Dirac series for complex 𝐸7

Author:

Dong Chao-Ping1,Wong Kayue Daniel2ORCID

Affiliation:

1. School of Mathematical Sciences , Soochow University , Suzhou 215006 , P. R. China

2. School of Science and Engineering , The Chinese University of Hong Kong , Shenzhen , Guangdong 518172 , P. R. China

Abstract

AbstractThis paper classifies the Dirac series for complexE7E_{7}. As applications, we verify a few conjectures raised in 2011, 2019 and 2020 for this exceptional Lie group. In particular, according to Conjecture 1.1 of Barbasch and Pandžić [Dirac cohomology and unipotent representations of complex groups,Noncommutative Geometry and Global Analysis, Contemp. Math. 546, American Mathematical Society, Providence (2011), 1–22], our classification should be helpful for understanding the unitary dual of complexE7E_{7}.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,General Mathematics

Cited by 2 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Dirac series for complex classical Lie groups: A multiplicity-one theorem;Advances in Mathematics;2022-07

2. Dirac Series of GL(n, ℝ);International Mathematics Research Notices;2022-06-02

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