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arXiv · 0710.2627

Branching integrals and Casselman phenomenon

Yury A- Neretin
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Abstract

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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Yury A- Neretin. 2007-10-13. Branching integrals and Casselman phenomenon. https://doi.org/10.1007/978-3-7643-9906-1_21

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