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

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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 1

Keywords

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

ASJC Scopus subject areas

  • Algebra and Number Theory

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