Unitary representations of the universal cover of SU(1,1) and tensor products

Details Unitary representations of the universal cover of SU(1,1) and tensor products Unitary representations of the universal cover of SU(1,1) and tensor products

2011-02-02

arxiv.org/abs/1102.0374v1

Mathematics

Representation Theory

38 pages

Scientific paper

In this paper we initiate a study of the relation between weight modules for simple Lie algebras and unitary representations of the corresponding simply-connected Lie groups. In particular we consider in detail from this point of view the universal covering group of SU(1,1), including new results on the discrete part of tensor products of irreducible representations. As a consequence of these results, we show that the set of smooth vectors of the tensor product intersects trivially some of the representations in the discrete spectrum.

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