On branching laws of Speh representations

2021/10/27 by Nozomi Ito, Ito, Nozomi
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.2110.14145

openalex publication_date 2021/10/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider the branching law of the Speh representation Sp(π,n+l) of GL_2n+2l with respect to the block diagonal subgroup GL_n\timesGL_n+2l for any irreducible generic representation π of GL₂ over any p-adic field. We use the Shalika model of Sp(π,n) to construct certain zeta integrals, which were defined by Ginzburg and Kaplan independently, and study them. Finally, using these zeta integrals, we obtain a nonzero GL_n\timesGL_n+2l-map from Sp(π,n+l) to τ\boxtimesτ^\veeχ_π\timesSp(π, l) for any irreducible representation τ of GL_n. These results form part of the local theory of the Miyawaki lifting for unitary groups.

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