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On the Tempered Spectrum of Quasi-Split Classical Groups II

Published online by Cambridge University Press:  20 November 2018

David Goldberg  and
Freydoon Shahidi
David Goldberg
Affiliation:
Department of Mathematics Purdue University West Lafayette, Indiana 47907 U.S.A.
Freydoon Shahidi
Affiliation:
Department of Mathematics Purdue University West Lafayette, Indiana 47907 U.S.A.
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Abstract

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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 $M\simeq \text{G}{{\text{L}}_{n}}\left( E \right)\times {{U}_{m}}\left( F \right)$, with $n\,\equiv \,m\,\left( \bmod \,2 \right)$. This, along with earlier work, determines the poles of the local Rankin-Selberg product $L$-function $L\left( s,\,{\tau }'\,\times \,\tau \right)$, with ${\tau }'$ an irreducible unitary supercuspidal representation of $\text{G}{{\text{L}}_{n}}\left( E \right)$ and $\tau $ a generic irreducible unitary supercuspidal representation of ${{U}_{m}}\left( F \right)$. The results are interpreted using the theory of twisted endoscopy.

Keywords

22E5011S70
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 53 , Issue 2 , 01 April 2001 , pp. 244 - 277
Copyright
Copyright © Canadian Mathematical Society 2001

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