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
Spherical Functions with Respect to the Semisimple Symmetric Pair $(Sp(2,\Bbb R),SL(2,\Bbb R) × SL(2,\Bbb R))$
jms060107.pdf
(322.33KB)
