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Analysis and Mathematical Physics pp 427–439Cite as

Ramified Integrals, Casselman Phenomenon, and Holomorphic Continuations of Group Representations

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Abstract

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.

Keywords

  • Irreducible Representation
  • Unitary Representation
  • Spinor Representation
  • Maximal Compact Subgroup
  • Principal Series

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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Author information

Authors and Affiliations

  1. Math. Dept., University of Vienna, Nordbergstrasse, 15, Vienna, Austria

    Yuri A. Neretin

  2. Institute for Theoretical and Experimental Physics, Bolshaya Cheremushkinskaya 25, Moscow, 117259, Russia

    Yuri A. Neretin

Authors
  1. Yuri A. Neretin
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Editor information

Editors and Affiliations

  1. Department of Mathematics, Royal Institute of Technology (KTH), 100 44, Stockholm, Sweden

    Björn Gustafsson

  2. Department of Mathematics, University of Bergen, Johannes Brunsgate 12, 5008, Bergen, Norway

    Alexander Vasil’ev

Additional information

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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