Spherical functions on Sp2as a spherical homogeneous Sp2 × (Sp1)2-space

    Research output: Contribution to journalArticle

    6 Citations (Scopus)

    Abstract

    We investigate spherical functions on Sp2 as a spherical homogeneous G = Sp2 × (Sp1)2-space over a p-adic field k, which form a 4-dimensional vector space for each eigenvalue given by Satake parameter. Explicit expressions of spherical functions and Cartan decomposition of Sp2 are given. Using spherical transform, we determine Hecke module structure of the Schwartz-Bruhat space S(K\Sp2), which is free of rank 4.

    Original languageEnglish
    Pages (from-to)238-286
    Number of pages49
    JournalJournal of Number Theory
    Volume112
    Issue number2
    DOIs
    Publication statusPublished - 2005 Jun

    Fingerprint

    Spherical Functions
    P-adic Fields
    Vector space
    Transform
    Eigenvalue
    Decompose
    Module

    Keywords

    • P-adic field
    • Spherical function
    • Spherical homogeneous space

    ASJC Scopus subject areas

    • Algebra and Number Theory

    Cite this

    Spherical functions on Sp2as a spherical homogeneous Sp2 × (Sp1)2-space. / Hironaka, Yumiko.

    In: Journal of Number Theory, Vol. 112, No. 2, 06.2005, p. 238-286.

    Research output: Contribution to journalArticle

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