Spherical functions on the space of p-adic unitary hermitian matrices

Yumiko Hironaka, Yasushi Komori

研究成果: Article査読

1 被引用数 (Scopus)

抄録

We investigate the space X of unitary hermitian matrices over 𝔭-adic fields through spherical functions. First we consider Cartan decomposition of X, and give precise representatives for fields with odd residual characteristic, i.e. 2 ∉ 𝔭. From Sec. 2.2 till the end of Sec. 4, we assume odd residual characteristic, and give explicit formulas of typical spherical functions on X, where Hall-Littlewood symmetric polynomials of type Cn appear as a main term, parametrization of all the spherical functions. By spherical Fourier transform, we show that the Schwartz space $\mathcal{S}(K{\backslash}X)$ is a free Hecke algebra $\mathcal{H}(G,K)$-module of rank 2n, where 2n is the size of matrices in X, and give the explicit Plancherel formula on $\mathcal{S}(K{\backslash}X)$.

本文言語English
ページ(範囲)513-558
ページ数46
ジャーナルInternational Journal of Number Theory
10
2
DOI
出版ステータスPublished - 2014 3

ASJC Scopus subject areas

  • 代数と数論

フィンガープリント

「Spherical functions on the space of p-adic unitary hermitian matrices」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。

引用スタイル