Generalized Whittaker functions for degenerate principal series of $GL(4,\R)$

Details Generalized Whittaker functions for degenerate principal series of $GL(4,\R)$ Generalized Whittaker functions for degenerate principal series of $GL(4,\R)$

2008-09-12

arxiv.org/abs/0809.2127v1

Mathematics

Representation Theory

54 pages

Scientific paper

We give a characterization of a generalized Whittaker model of a degenerate principal series representation of $GL(n,\R)$ as the kernel of some differential operators. By this characterization, we investigate some examples on $GL(4,\R)$. We obtain the dimensions of the generalized Whittaker models and give their basis in terms of hypergeometric functions of one and two variables. We show the multiplicity one of the generalized Whittaker models by using the theory of hypergeometric functions.

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