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PARITY OF THE LANGLANDS PARAMETERS OF CONJUGATE SELF-DUAL REPRESENTATIONS OF $\text{GL}(n)$ AND THE LOCAL JACQUET–LANGLANDS CORRESPONDENCE

Part of: Discontinuous groups and automorphic forms Lie groups Arithmetic algebraic geometry

Published online by Cambridge University Press:  19 February 2019

Yoichi Mieda
Yoichi Mieda*
Affiliation:
Graduate School of Mathematical Sciences, The University of Tokyo, 3–8–1 Komaba, Meguro-ku, Tokyo, 153–8914, Japan ([email protected])
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Abstract

We determine the parity of the Langlands parameter of a conjugate self-dual supercuspidal representation of $\text{GL}(n)$ over a non-archimedean local field by means of the local Jacquet–Langlands correspondence. It gives a partial generalization of a previous result on the self-dual case by Prasad and Ramakrishnan.

Keywords

local Langlands correspondencelocal Jacquet–Langlands correspondenceLubin–Tate space

MSC classification

Primary: 11F70: Representation-theoretic methods; automorphic representations over local and global fields
Secondary: 11G25: Varieties over finite and local fields 22E50: Representations of Lie and linear algebraic groups over local fields
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 19 , Issue 6 , November 2020 , pp. 2017 - 2043
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Copyright
© Cambridge University Press 2019

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