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  1. 121 数理科学研究科
  2. Journal of Mathematical Sciences, the University of Tokyo
  3. 8
  4. 4
  1. 0 資料タイプ別
  2. 30 紀要・部局刊行物
  3. Journal of Mathematical Sciences, the University of Tokyo
  4. 8
  5. 4

Real Shintani Functions on $U(n,1)$

http://hdl.handle.net/2261/1171
e634fc79-cbe4-4fee-a67a-abb5c21d36ee
名前 / ファイル ライセンス アクション
jms080403.pdf jms080403.pdf (534.6 kB)
Item type 紀要論文 / Departmental Bulletin Paper(1)
公開日 2008-03-04
タイトル
タイトル Real Shintani Functions on $U(n,1)$
言語
言語 eng
キーワード
主題 shintani functions
主題Scheme Other
資源タイプ
資源 http://purl.org/coar/resource_type/c_6501
タイプ departmental bulletin paper
著者 Tsuzuki, Masao

× Tsuzuki, Masao

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Tsuzuki, Masao

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抄録
内容記述タイプ Abstract
内容記述 Let $G=\sU(n,1)$ and $H=\sU(n-1,1) × \sU(1)$ with $n\geqslant 2$. We realize $H$ as a closed subgroup of $G$, so that $(G,H)$ forms a semisimple symmetric pair of rank one. For irreducible representations $π$ and $η$ of $G$ and $H$ respectively, we consider the space ${\cal I}_{η,π}={\rm Hom}_{\g_\C,K} (π,{\rm Ind}_H^G(η))$ with $K$ a maximal compact subgroup in $G$ and $\g_\C$ the complexified Lie algebra of $G$. The functions that belong to ${\rm Im}(Φ)$ for some $Φ\in {\cal I}_{η,π}$ will be called the {\it Shintani functions}. We prove that ${\rm dim}_\C{\cal I}_{η,π}\leqslant 1$ for any $π $ and any $η$, giving an explicit formula of the Shintani functions that generate a \lq corner\rq\ $K$-type of $π$ in terms of Gaussian hypergeometric series. We also give an explicit formula of corner $K$-type matrix coefficients of $π$ in the usual sense.
書誌情報 Journal of mathematical sciences, the University of Tokyo

巻 8, 号 4, p. 609-688, 発行日 2001
ISSN
収録物識別子タイプ ISSN
収録物識別子 13405705
書誌レコードID
収録物識別子タイプ NCID
収録物識別子 AA11021653
フォーマット
内容記述タイプ Other
内容記述 application/pdf
日本十進分類法
主題 415
主題Scheme NDC
Mathematical Reviews Number
MR1868294
Mathmatical Subject Classification
11F70(MSC1991)
Mathmatical Subject Classification
22E46(MSC1991)
Mathmatical Subject Classification
33C05(MSC1991)
Mathmatical Subject Classification
11F67(MSC1991)
出版者
出版者 Graduate School of Mathematical Sciences, The University of Tokyo
原稿受領日
2000-11-06
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