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An arithmetic property of intertwining operators for p-adic groups

Part of: Discontinuous groups and automorphic forms Lie groups

Published online by Cambridge University Press:  17 September 2021

A. Raghuram Open the ORCID record for A. Raghuram [Opens in a new window]
A. Raghuram*
Affiliation:
Department of Mathematics, Fordham University at Lincoln Center, New York, NY 10023, USA
*
e-mail: araghuram@fordham.edu
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Abstract

The main aim of this article is to show that normalised standard intertwining operator between induced representations of p-adic groups, at a very specific point of evaluation, has an arithmetic origin. This result has applications to Eisenstein cohomology and the special values of automorphic L-functions.

Keywords

intertwining operatorsp-adic groupspoint of evaluationarithmeticity

MSC classification

Primary: 22E50: Representations of Lie and linear algebraic groups over local fields
Secondary: 22E55: Representations of Lie and linear algebraic groups over global fields and adèle rings 11F67: Special values of automorphic $L$-series, periods of modular forms, cohomology, modular symbols 11F70: Representation-theoretic methods; automorphic representations over local and global fields

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Type
Article
Information
Canadian Journal of Mathematics , Volume 75 , Issue 1 , February 2023 , pp. 83 - 107
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Copyright
© Canadian Mathematical Society 2021

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