Spherical Shalika models on PGU_2,2 and the theta correspondence for (PGSp₄,PGU_2,2)

2023/11/09 by Antonio Cauchi, Cauchi, Antonio, Armando Gutierrez Terradillos +1
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2311.05759

openalex publication_date 2023/11/09 · openalex created_date 2023/11/14 · openalex updated_date 2026/07/28

Abstract

We study Shalika models for generic unramified representations of PGU_2,2 over non-archimedean local fields of characteristic zero. We show that they are unique up to constant by means of the theta correspondence for (PGSp₄,PGU_2,2). We then prove a Casselman-Shalika formula which relates the values of spherical Shalika functionals on \rm PGU_2,2 to the values of finite dimensional complex representations of the dual group of PGSp₄.

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