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.
- Irreducible Representation
- Unitary Representation
- Spinor Representation
- Maximal Compact Subgroup
- Principal Series
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Supported by the grant FWF, project P19064, Russian Federal Agency for Nuclear Energy, Dutch grant NWO.047.017.015, and grant JSPS-RFBR-07.01.91209.
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To Mark Iosifovich Graev on his 85th birthday
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Neretin, Y.A. (2009). Ramified Integrals, Casselman Phenomenon, and Holomorphic Continuations of Group Representations. In: Gustafsson, B., Vasil’ev, A. (eds) Analysis and Mathematical Physics. Trends in Mathematics. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-9906-1_21
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