Local newforms for generic representations of unramified \rm U_2n+1 and Rankin-Selberg integrals

2022/07/05 by Yao Cheng, Cheng, Yao · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2207.02118

openalex publication_date 2022/07/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Recently Atobe-Oi-Yasuda established the newform theory for irreducible tempered generic representations of unramified \rm U_2n+1 over non-archimedean local fields. In this paper we extend their result to every irreducible generic representations and compute the dimensions of the spaces of oldforms. We also compute the Rankin-Selberg integrals attached to newforms and oldforms under a natural assumption on the γ-factors defined by these integrals.

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