Distinction and Asai L-functions for generic representations of general linear groups over p-adic fields

2009/02/18 by Nadir Matringe, Matringe, Nadir
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.0902.3061

openalex publication_date 2009/02/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let K/F be a quadratic extension of p-adic fields, and n a positive integer. A smooth irreducible representation of the group GL(n,K) is said to be distinguished, if it admits on its space a nonzero GL(n,F)-invariant linear form. In the present work, we classify genric distinguished representations of the group GL(n,K) in terms of inducing quasi-square-integrable representations. This has as a consequence the truth of the expected equality between the Rankin-Selberg type Asai L-function of a generic representation, and the Asai L-function of its Langlands parameter.

Citations

• Conjectures about distinction and Asai L-functions of generic representations of general linear groups over local fields

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