Uniqueness of Rankin-Selberg periods

2013/11/21 by Fulin Chen, Chen, Fulin, Binyong Sun +1 · 2 citations
Mathematics · #22E50 #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.1311.5321

openalex publication_date 2013/11/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let k be a local field of characteristic zero. Rankin-Selberg's local zeta integrals produce linear functionals on generic irreducible admissible smooth representations of GL_n(k)× GL_r(k), with certain invariance properties. We show that up to scalar multiplication, these linear functionals are determined by the invariance properties.

Citations

• Symplectic local root numbers, central critical L-values, and restriction problems in the representation theory of classical groups
• Rankin-Selberg Convolutions

Cited by

• Bound on multiplicities of symmetric pairs over p-adic fields
• Non-tempered Gan-Gross-Prasad conjecture for Archimedean general linear groups

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