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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.

Information

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

References

[ 1 ] Andriaov, A. N., Spherical functions for GLn over local fields, and summation of Hecke series, Math USSR Sbornik., 12 (1970), 429–451.Google Scholar
[ 2 ] Andrianov, A. N., On factorization of Hecke polynomials for the symplectic group of genus n , Math USSR Sbornik., 33 (1977), 343–373.Google Scholar
[ 3 ] Bruhat, F., and Tits, J., Groupes reductifs sur un corps local, Publ. Math. Inst. Hautes Etudes Sci., 41 (1972), 5–251.Google Scholar
[ 4 ] Casselman, W., The unramified principal series of p-adic groups I, The spherical function, Compositio Math., 40 (1980), 387–406.Google Scholar
[ 5 ] Hijikata, H., Maximal compact subgroups of some p-adic classical groups, Yale University.Google Scholar
[ 6 ] Macdonald, I. G., Spherical functions on a group of p-adic type, Advanced Study of Math. Madras., (1970).Google Scholar
[ 7 ] Satake, I., Theory of spherical functions on reductive algebraic groups over p-adic fields, I.H.E.S., 18 (1963).Google Scholar
[ 8 ] Springer, T. A., Linear algebraic groups, Birkhauser.Google Scholar
[ 9 ] Tits, J., Reductive groups over local fields, Proc. of Sympoia in Pure Math., 33 part 1, A.M.S., (1979), 29–69.Google Scholar