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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, 11S70 show english descriptions Representations of Lie and linear algebraic groups over local fields [See also 20G05]
$K$-theory of local fields [See also 19Fxx]
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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