Stability of the local gamma factor in the unitary case

Eliot Brenner

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Stability of the local gamma factor in the unitary case

Eliot Brenner

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Abstract

Rallis and Soudry have proven the stability under twists by highly ramified characters of the local gamma factor arising from the doubling method, in the case of a symplectic group or orthogonal group G over a local non-archimedean field F of characteristic zero, and a representation of G, which is not necessarily generic. This paper extends their arguments to show the stability in the case when G is a unitary group over a quadratic extension E of F, thereby completing the proof of the stability for classical groups. This stability property is important in Cogdell, Piatetski-Shapiro, and Shahidi's use of the converse theorem to prove the existence of a weak lift from automorphic, cuspidal, generic representations of G(A) to automorphic representations of GL(n,A) for appropriate n, to which references are given in the paper of Rallis and Soudry.

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BibTeX RIS

Eliot Brenner. 2006-08-03. Stability of the local gamma factor in the unitary case. https://arxiv.org/abs/math/0608101

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