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Dirac series for complex 𝐸7

  • Chao-Ping Dong and Kayue Daniel Wong ORCID logo EMAIL logo
Published/Copyright: March 31, 2022

Abstract

This paper classifies the Dirac series for complex E7. 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 complex E7.

MSC 2010: 22E46

Award Identifier / Grant number: 12171344

Award Identifier / Grant number: 11901491

Funding statement: C.-P. Dong is supported by the National Natural Science Foundation of China (grant 12171344). K. D. Wong is supported by the National Natural Science Foundation of China (grant 11901491) and the Presidential Fund of CUHK(SZ).

Acknowledgements

Our sincere gratitude is expressed to Professor Vogan for testing the unitarity of representation (v) in Section 6, and to Professor Adams for sharing his knowledge on the model orbit 4A1 in Section 6 with us. We also thank Dr. Luan for helping us considering the branching (7.2). We sincerely thank an anonymous referee for his/her great patience in reading this manuscript and offering us excellent suggestions.

  1. Communicated by: Freydoon Shahidi

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Received: 2021-10-27
Revised: 2022-02-27
Published Online: 2022-03-31
Published in Print: 2022-07-01

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