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On generalized Whittaker functions on Siegel’s upper half space of degree 2

Published online by Cambridge University Press:  22 January 2016

S. Niwa
S. Niwa*
Affiliation:
Nagoya City College of Child Education, Owariasahi, 488, Japan
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In [5], H. Maass showed that the dimension of a space of generalized Whittaker functions satisfying certain system of differential equations on Siegel’s upper half space H2 of degree 2 is three. First of all, we shall investigate the structure of a space of generalized Whittaker functions which are eigen functions for the algebra of invariant differential operators on H2. The theory of generalized Whittaker functions is discussed in Yamashita [12], [13], [14], [15] with full generality. But, we will get an outlook of the space of generalized Whittaker functions by using elementary calculus instead of representation theory of Lie groups.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 121 , March 1991 , pp. 171 - 184
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1991

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