Ramified Integrals, Casselman Phenomenon, and Holomorphic Continuations of Group Representations
Let G be a real semisimple Lie group, K its maximal compact subgroup, and Gc its complexification. It is known that all K-finite matrix elements on G admit holomorphic continuations to branching functions on Gc having singularities at a prescribed divisor. We propose a geometric explanation of this phenomenon.
KeywordsIrreducible Representation Unitary Representation Spinor Representation Maximal Compact Subgroup Principal Series
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