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}.
Subject
Applied Mathematics,General Mathematics
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