Asymptotic K-Support and Restrictions of Representations

Details Asymptotic K-Support and Restrictions of Representations Asymptotic K-Support and Restrictions of Representations

2009-05-07

arxiv.org/abs/0905.1009v1

Mathematics

Representation Theory

12 pages

Scientific paper

In the late nineties T. Kobayashi wrote a series of papers in which he established a criterion for the discrete decomposablity of restrictions of unitary representations of reductive Lie groups to reductive subgroups. A key tool in the proof of sufficiency of his criterion was the use of the theory of hyperfunctions to study the microlocal behavior of characters of restrictions to compact subgroups. In this paper we show how to replace this tool by microlocal analysis in the $C^\infty$ category.

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