On the Tempered Spectrum of Quasi-Split Classical Groups II

David Theo Goldberg, Freydoon Shahidi

Type: Article

Publication Date: 2001-04-01

Citations: 17

DOI: https://doi.org/10.4153/cjm-2001-011-7

Abstract

Abstract We determine the poles of the standard intertwining operators for a maximal parabolic subgroup of the quasi-split unitary group defined by a quadratic extension E/F of p -adic fields of characteristic zero. We study the case where the Levi component M ≃ GL n ( E ) × U m ( F ), with n ≡ m (mod 2). This, along with earlier work, determines the poles of the local Rankin-Selberg product L -function L(s, t′ × τ), with t′ an irreducible unitary supercuspidal representation of GL n ( E ) and τ a generic irreducible unitary supercuspidal representation of U m ( F ). The results are interpreted using the theory of twisted endoscopy.

Locations

Canadian Journal of Mathematics - View - PDF

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+	The classification of involutions of simple algebraic groups	1987	T. A. Springer
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+	Invariant Harmonic Analysis on the Schwartz Space of a Reductive p-ADIC Group	1991	Laurent Clozel
+	Reducibility of generalized principal series representations of $U(2, 2)$ via base change	1993	David Theo Goldberg
+ PDF Chat	Harmonic analysis on reductive 𝑝-adic groups	1973	Harish-chandra Harish-Chandra
+ PDF Chat	Harmonic Analysis on Reductive p-adic Groups	1970	Harish-chandra Harish-Chandra