Multiplicity one for the pair (GL(n,D),GL(n,E))

2021/05/23 by Hengfei Lu, Lu, Hengfei · 1 citation
Mathematics · #22E50 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry and Number Theory #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2105.10855

openalex publication_date 2021/05/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let F be a local field of characteristic zero. Let D be a quaternion algebra over F. Let E be a quadratic field extension of F. Let μ be a character of GL(1,E). We study the distinction problem for the pair (GL(n,D), GL(n,E)) and we prove that any bi-(GL(n,E), μ)-equivariant tempered generalized function on GL(n,D) is invariant with respect to an anti-involution. Then it implies that dimHom(π,μ) is at most 1 by the generalized Gelfand-Kazhdan criterion. Thus we give a new proof to the fact that (GL(2n,F),GL(n,E)) is a Gelfand pair when μ is trivial and D splits.

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• Distinguished representations for \rmSL(n,F)

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