Functional equations of spherical functions on p-adic homogeneous spaces

    Research output: Contribution to journalArticle

    2 Citations (Scopus)

    Abstract

    Let G be a connected reductive linear algebraic group and X a G-homogeneous affine algebraic variety both defined over a p-adic field k, where we assume a minimal k-parabolic subgroup of G 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 Universität Hamburg
    Volume75
    Issue number1
    DOIs
    Publication statusPublished - 2005 Dec

    Fingerprint

    Spherical Functions
    Homogeneous Space
    P-adic
    Functional equation
    Prehomogeneous Vector Spaces
    Linear Algebraic Groups
    P-adic Fields
    Parabolic Subgroup
    Algebraic Variety
    Riemann zeta function
    Orbit

    Keywords

    • p-adic homogeneous space
    • prehomogeneous vector space
    • Spherical function

    ASJC Scopus subject areas

    • Mathematics(all)

    Cite this

    @article{d5a8f88ee7104603b1b4f8a524f78d5e,
    title = "Functional equations of spherical functions on p-adic homogeneous spaces",
    abstract = "Let G be a connected reductive linear algebraic group and X a G-homogeneous affine algebraic variety both defined over a p-adic field k, where we assume a minimal k-parabolic subgroup of G 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.",
    keywords = "p-adic homogeneous space, prehomogeneous vector space, Spherical function",
    author = "Yumiko Hironaka",
    year = "2005",
    month = "12",
    doi = "10.1007/BF02942047",
    language = "English",
    volume = "75",
    pages = "285--311",
    journal = "Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg",
    issn = "0025-5858",
    publisher = "Springer Verlag",
    number = "1",

    }

    TY - JOUR

    T1 - Functional equations of spherical functions on p-adic homogeneous spaces

    AU - Hironaka, Yumiko

    PY - 2005/12

    Y1 - 2005/12

    N2 - Let G be a connected reductive linear algebraic group and X a G-homogeneous affine algebraic variety both defined over a p-adic field k, where we assume a minimal k-parabolic subgroup of G 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.

    AB - Let G be a connected reductive linear algebraic group and X a G-homogeneous affine algebraic variety both defined over a p-adic field k, where we assume a minimal k-parabolic subgroup of G 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.

    KW - p-adic homogeneous space

    KW - prehomogeneous vector space

    KW - Spherical function

    UR - http://www.scopus.com/inward/record.url?scp=33749420654&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=33749420654&partnerID=8YFLogxK

    U2 - 10.1007/BF02942047

    DO - 10.1007/BF02942047

    M3 - Article

    VL - 75

    SP - 285

    EP - 311

    JO - Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg

    JF - Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg

    SN - 0025-5858

    IS - 1

    ER -