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Complex integral geometry and harmonic analysis on real Lie groups.
Colloquium| Speaker: | Professor Simon Gindikin, Rutgers University, New Brunswick |
| Location: | 693 Kerr |
| Start time: | Mon, Mar 15 1999, 4:10PM |
Harmonic analysis in SL(2, C) is equivalent to the consideration of a integral t ransform - the integration of functions on C^3 along lines intersecting hyperbol a. This reduction can be generalized on arbitrary complex semisimple Lie groups or Riemann symmetric spaces (the horospherical trasform of Gelfand and Graev). T he old problem of Gelfand was to find an analog of these constructions for real groups starting of SL(2, R). We will explain on the example of the last group ho w it is possible to solve this problem using by complex horospheres without rea l points and discuss possible generalizations and applications.