On the Tempered Spectrum of Quasi-Split Classical Groups II

Goldberg, David ; Shahidi, Freydoon

Canadian journal of mathematics, Tome 53 (2001) no. 2, pp. 244-277

Résumé

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.

Détail

DOI : 10.4153/CJM-2001-011-7

Mots-clés : 22E50, 11S70

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