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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. 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Real Shintani Functions on $U(n,1)$
http://hdl.handle.net/2261/1171
http://hdl.handle.net/2261/1171e634fc79-cbe4-4fee-a67a-abb5c21d36ee
名前 / ファイル | ライセンス | アクション |
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jms080403.pdf (534.6 kB)
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Item type | 紀要論文 / Departmental Bulletin Paper(1) | |||||
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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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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 |
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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 |