Functional equations of spherical functions on p-adic homogeneous spaces

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2 Citations (Scopus)

Abstract

Let dubble struck G sign be a connected reductive linear algebraic group and dubble struck X sign a dubble struck G sign-homogeneous affine algebraic variety both defined over a p-adic field k, where we assume a minimal k-parabolic subgroup of dubble struck G sign acts with open orbit. We are interested in spherical functions on X = X(k). In the present papaer, we give a unified method to obtain functional equations of spherical functions on X under the condition (AF) in the introduction, and explain functional equations are reduced to those of p-adic local zeta functions of small prehomogeneous vector spaces of limited type.

Original languageEnglish
Pages (from-to)285-311
Number of pages27
JournalAbhandlungen aus dem Mathematischen Seminar der Universitat Hamburg
Volume75
DOIs
Publication statusPublished - 2005 Dec 1

Keywords

  • P-adic homogeneous space
  • Prehomogeneous vector space
  • Spherical function

ASJC Scopus subject areas

  • Mathematics(all)

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