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July 2020 On some relatively cuspidal representations: Cases of Galois and inner involutions on ${\rm GL}_n$
Shin-ichi Kato, Keiji Takano
Osaka J. Math. 57(3): 711-736 (July 2020).

Abstract

Relatively cuspidal representations attached to a $p$-adic symmetric space $G/H$ are thought of as the building blocks for all the irreducible $H$-distinguished representations of $G$. This work provides certain new examples of relatively cuspidal representations. We study three examples of symmetric spaces; ${\rm GL}_n(E)/{\rm GL}_n(F)$, ${\rm GL}_{2m}(F)/{\rm GL}_m(E)$, and ${\rm GL}_n(F)/\bigl({\rm GL}_{n-r}(F)\times{\rm GL}_r(F)\bigr)$ where $E/F$ is a quadratic extension of $p$-adic fields. Those representations are given by induction from cuspidal distinguished representations of particular kinds of parabolic subgroups stable under the involution.

Citation

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Shin-ichi Kato. Keiji Takano. "On some relatively cuspidal representations: Cases of Galois and inner involutions on ${\rm GL}_n$." Osaka J. Math. 57 (3) 711 - 736, July 2020.

Information

Published: July 2020
First available in Project Euclid: 13 July 2020

zbMATH: 07224930
MathSciNet: MR4121785

Subjects:
Primary: 22E50
Secondary: 11F70, 20G05, 22E35

Rights: Copyright © 2020 Osaka University and Osaka City University, Departments of Mathematics

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Vol.57 • No. 3 • July 2020
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