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

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概要

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• 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.

• 東京大学の論文

著者

• Moriyama Tomonori

  Graduate School Of Mathematical Sciences The University Of Tokyo

• Moriyama Tomonori

  Graduate School of Mathematical Sciences, The University of Tokyo

関連論文

• A Remark on Whittaker Functions on Sp(2,R)
• Spherical Functions with Respect to the Semisimple Symmetric Pair $(Sp(2,\Bbb R),SL(2,\Bbb R) × SL(2,\Bbb R))$

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