Spherical Functions with Respect to the Semisimple Symmetric Pair (Sp(2,\Bbb R),SL(2,\Bbb R) Ã SL(2,\Bbb R))
Vol. 6 (1999), No. 1, Page 127--179.
Moriyama, Tomonori
Spherical Functions with Respect to the Semisimple Symmetric Pair (Sp(2,\Bbb R),SL(2,\Bbb R) Ã SL(2,\Bbb R))
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Abstract:
Let Ï 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 Ï 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.
Mathematics Subject Classification (1991): Primary 11F70; Secondary 22E30
Mathematical Reviews Number: MR1683317
Received: 1997-12-01
