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

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