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 タイトル: Spherical Functions with Respect to the Semisimple Symmetric Pair \$(Sp(2,\Bbb R),SL(2,\Bbb R) × SL(2,\Bbb R))\$ 著者: Moriyama, Tomonori 発行日: 1999年 出版者: Graduate School of Mathematical Sciences, The University of Tokyo 掲載誌情報: Journal of Mathematical Sciences, The University of Tokyo. Vol. 6 (1999), No. 1, Page 127-179 抄録: Let \$π\$ be a generalized principal series representation with respect to the Jacobi parabolic subgroup or a large discrete series representation of \$G=Sp(2,\Bbb R)\$. A spherical function is the image of a \$K\$-finite vector by the intertwining operator from \$π\$ to the {\rep } induced from an irreducible unitary representation of \$SL(2,\Bbb R)^2\$ in \$G\$. We obtain differential equations for the spherical functions except for a few cases. We write down the solutions of these differential equations by means of the Gaussian hypergeometric functions. URI: http://hdl.handle.net/2261/1246 ISSN: 13405705 出現カテゴリ: Journal of Mathematical Sciences, the University of TokyoJournal of Mathematical Sciences, the University of Tokyo

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