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

Kazuki Hiroe

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

Representation Theory 2008-09-15 v1

Authors: Kazuki Hiroe

Abstract

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.

Keywords

generalized Whittaker functions degenerate principal series GL(4,R) differential operators hypergeometric functions multiplicity one

Cite

@article{arxiv.0809.2127,
  title  = {Generalized Whittaker functions for degenerate principal series of $GL(4,\R)$},
  author = {Kazuki Hiroe},
  journal= {arXiv preprint arXiv:0809.2127},
  year   = {2008}
}

Comments

54 pages

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