Complex integral geometry

Rutgers University New Brunswick, New Brunswick NJ

Investigators

Abstract

Abstract Gindikin The focus of the proposal is the development of a method of complex horospheras for real affine symmetric spaces, including real semisimple Lie groups. We anticipate to apply this method to the construction of the models of series of representations and to the decomposition of the regular representations on series on the language of Hardy spaces of cohomology. As one of application we hope to give an integral geometrical proof of the product-formula for c-function of Harishi-Chandra. Another direction of my research is the investigation of geometrical and analytic properties of the crowns of Riemann symmetric spaces - their canonical Stein neighborhoods. Integral geometry is a branch of geometrical analysis which investigates integral transforms associated with different geometrical structures. The principal challenge is to find a geometrical setting, more general than the group one, where it is possible to develop a non-abelian harmonic analysis. Another direction considers complex constructions responsible for the geometry of real affine symmetric spaces. Such phenomena have roots in classical geometry of Poncelet and Pluecker.