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Twisted GGP problems and conjectures

Part of: Lie groups Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  31 July 2023

Wee Teck Gan ,
Benedict H. Gross  and
Dipendra Prasad
Wee Teck Gan
Affiliation:
National University of Singapore, Singapore 119076, Singapore [email protected]
Benedict H. Gross
Affiliation:
Department of Mathematics, University of California San Diego, La Jolla, CA 92093, USA [email protected]
Dipendra Prasad
Affiliation:
Indian Institute of Technology Bombay, Powai, Mumbai 400076, India [email protected]
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Abstract

In a series of three earlier papers, we considered a family of restriction problems for classical groups (over local and global fields) and proposed precise answers to these problems using the local and global Langlands correspondence. These restriction problems were formulated in terms of a pair $W \subset V$ of orthogonal, Hermitian, symplectic, or skew-Hermitian spaces. In this paper, we consider a twisted variant of these conjectures in one particular case: that of a pair of skew-Hermitian spaces $W = V$.

Keywords

branching lawsreal and p-adic groupsclassical groupsunitary groupsWeil representationGGP conjecturesperiod integralsskew-Hermitian spacesLanglands parameterstempered representations

MSC classification

Primary: 11F70: Representation-theoretic methods; automorphic representations over local and global fields
Secondary: 22E55: Representations of Lie and linear algebraic groups over global fields and adèle rings
Type
Research Article
Information
Compositio Mathematica , Volume 159 , Issue 9 , September 2023 , pp. 1916 - 1973
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Copyright
© 2023 The Author(s). The publishing rights in this article are licensed to Foundation Compositio Mathematica under an exclusive licence

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Footnotes

WTG is partially supported by an MOE Tier 1 grant R-146-000-320-114. DP thanks the Science and Engineering Research Board of the Department of Science and Technology, India for its support through the JC Bose National Fellowship of the Govt. of India, project number JBR/2020/000006. The paper was finalized when the two of us, WTG and DP, were at the Erwin Schrödinger Institute, Vienna in April 2022. We thank ESI for its excellent program which brought us together there.

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