Representation Theory and Random Point Processes

  • Alexei Borodin

    California Institute of Technology, Pasadena, United States
  • Grigori Olshanski

    Institute for Information Transmission Problems, Moscow, Russian Federation
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On a particular example we describe how to state and to solve the problem of harmonic analysis for groups with infinite-dimensional dual space. The representation theory for such groups differs in many respects from the conventional theory. We emphasize a remarkable connection with random point processes that arise in random matrix theory. The paper is an extended version of the second author’s talk at the Congress.