Spherical Functions on 2-adic Ramified Hermetian Spaces

2012/10/03 by Dror Ozeri, Ozeri, Dror
Mathematics · #Advanced Algebra and Geometry #FOS: Mathematics #Mathematical Dynamics and Fractals #Representation Theory (math.RT) #advanced mathematical theories #math.RT

paper · pdf · doi:10.48550/arxiv.1210.1083

arxiv created 2012/10/03 · openalex publication_date 2012/10/03 · arxiv updated 2012/10/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Y. Hironaka introduced the spherical functions on the p-adic space of Hermitian matrices. For the space of 2×2 Hermitian matrices, we complete Hironaka's work by also considering the case of a wildly ramified quadratic extension. We compute the spherical functions explicitly and obtain the functional equations.

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