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Spherical functions on orthogonal groups

Published online by Cambridge University Press:  22 January 2016

Yasuhiro Kajima
Yasuhiro Kajima*
Affiliation:
Graduate School of Polymathematics Nagoya University, Chikusa-ku, Nagoya, 464-01, Japan
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Let G be a p-adic connected reductive algebraic group and K a maximal compact subgroup of G. In [4], Casselman obtained the explicit formula of zonal spherical functions on G with respect to K on the assumption that K is special. It is known (Bruhat and Tits [3]) that the affine root system of algebraic group which has good but not special maximal compact subgroup is A1 C2, or Bn (n > 3), and all Bn-types can be realized by orthogonal groups. Here the assumption “good” is necessary for the Satake’s theory of spherical functions.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 141 , March 1996 , pp. 157 - 182
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1996

References

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