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# On the Tempered Spectrum of Quasi-Split Classical Groups II

Published:2001-04-01
Printed: Apr 2001
• David Goldberg
• Freydoon Shahidi
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## 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 $M \simeq \GL_n (E) \times U_m (F)$, with $n \equiv m$ $(\mod 2)$. This, along with earlier work, determines the poles of the local Rankin-Selberg product $L$-function $L(s, \tau' \times \tau)$, with $\tau'$ an irreducible unitary supercuspidal representation of $\GL_n (E)$ and $\tau$ a generic irreducible unitary supercuspidal representation of $U_m (F)$. The results are interpreted using the theory of twisted endoscopy.
 MSC Classifications: 22E50 - Representations of Lie and linear algebraic groups over local fields [See also 20G05] 11S70 - $K$-theory of local fields [See also 19Fxx]

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