Branching integrals and Casselman phenomenon

Details Branching integrals and Casselman phenomenon Branching integrals and Casselman phenomenon

2007-10-13

arxiv.org/abs/0710.2627v2

Mathematics

Representation Theory

13pp, an addendum is added

Scientific paper

Let $G$ be a real semisimple Lie group, $K$ its maximal complex subgroup, and $G_C$ its complexification. It is known that all the $K$-finite matrix elements on $G$ admit holomorphic continuation to branching functions on $G_C$ having singularities at the a prescribed divisor. We propose a geometric explanation of this phenomenon. The note also contsins a general survey of holomorphic continuations of infinite-dimensional representations.

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