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

Yumiko Hironaka

doi:10.1016/j.jnt.2004.08.012

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

Yumiko Hironaka^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

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 language	English
Pages (from-to)	238-286
Number of pages	49
Journal	Journal of Number Theory
Volume	112
Issue number	2
DOIs	https://doi.org/10.1016/j.jnt.2004.08.012
Publication status	Published - 2005 Jun
Externally published	Yes

Keywords

P-adic field
Spherical function
Spherical homogeneous space

ASJC Scopus subject areas

Algebra and Number Theory

Access to Document

10.1016/j.jnt.2004.08.012

Cite this

@article{cbe6750d93304a15805c454e6ede34b6,

title = "Spherical functions on Sp2as a spherical homogeneous Sp2 × (Sp1)2-space",

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.",

keywords = "P-adic field, Spherical function, Spherical homogeneous space",

author = "Yumiko Hironaka",

note = "Funding Information: Partly supported by Grant-in-Aid for Scientific Research, The Ministry of Education, Culture, Sports, Science and Technology, Japan. E-mail address: hironaka@edu.waseda.ac.jp.",

year = "2005",

month = jun,

doi = "10.1016/j.jnt.2004.08.012",

language = "English",

volume = "112",

pages = "238--286",

journal = "Journal of Number Theory",

issn = "0022-314X",

publisher = "Academic Press Inc.",

number = "2",

}

TY - JOUR

T1 - Spherical functions on Sp2as a spherical homogeneous Sp2 × (Sp1)2-space

AU - Hironaka, Yumiko

N1 - Funding Information: Partly supported by Grant-in-Aid for Scientific Research, The Ministry of Education, Culture, Sports, Science and Technology, Japan. E-mail address: hironaka@edu.waseda.ac.jp.

PY - 2005/6

Y1 - 2005/6

N2 - 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.

AB - 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.

KW - P-adic field

KW - Spherical function

KW - Spherical homogeneous space

UR - http://www.scopus.com/inward/record.url?scp=18744381290&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=18744381290&partnerID=8YFLogxK

U2 - 10.1016/j.jnt.2004.08.012

DO - 10.1016/j.jnt.2004.08.012

M3 - Article

AN - SCOPUS:18744381290

SN - 0022-314X

VL - 112

SP - 238

EP - 286

JO - Journal of Number Theory

JF - Journal of Number Theory

IS - 2

ER -