On the composition series of the standard Whittaker (g,K)-modules

Details On the composition series of the standard Whittaker (g,K)-modules On the composition series of the standard Whittaker (g,K)-modules

2011-02-24

arxiv.org/abs/1102.4966v1

Mathematics

Representation Theory

22pages

Scientific paper

For a real reductive linear Lie group G, the space of Whittaker functions is the representation space induced from a non-degenerate unitary character of the Iwasawa nilpotent subgroup. Defined are the standard Whittaker (g,K)-modules, which are K-admissible submodules of the space of Whittaker functions. We first determine the structures of them when the infinitesimal characters characterizing them are generic. As an example of the integral case, we determine the composition series of the standard Whittaker (g,K)-module when G is the group U(n,1) and the infinitesimal character is regular integral.

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