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.
雑誌名
Journal of mathematical sciences, the University of Tokyo
巻
6
号
1
ページ
127 - 179
発行年
1999
ISSN
13405705
書誌レコードID
AA11021653
フォーマット
application/pdf
日本十進分類法
415
Mathematical Reviews Number
MR1683317
Mathmatical Subject Classification
11F70(MSC1991)
22E30(MSC1991)
出版者
Graduate School of Mathematical Sciences, The University of Tokyo
原稿受領日
1997-12-01
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Spherical Functions with Respect to the Semisimple Symmetric Pair $(Sp(2,\Bbb R),SL(2,\Bbb R) × SL(2,\Bbb R))$
jms060107.pdf
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