Hypergeometric functions on reductive groups
Abstract
The Ahypergeometric system studied by I.M. Gelfand, M.I. Graev, A.V. Zelevinsky and the author, is defined for a set A of characters of an algebraic torus. In this paper we propose a generalization of the theory where the torus is replaced by an arbitrary reductive group H and A is a set of irreducible representations of H. The functions are thus defined on the space M_A of functions on H spanned by the matrix elements of representations from A. The properties of the system are related to the geometry of a certain algebraic variety X_A, which belongs to the class of group compactifications studied by De Concini and Procesi. We develop the theory of Euler integral representations for these generalized hypergeometric functions (with integrals taken over cycles in H). We also construct the analogs of hypergeometric series, by expanding the deltafunction along a subgroup into a power series and taking the termwise Fourier transform.
 Publication:

arXiv eprints
 Pub Date:
 November 1997
 DOI:
 10.48550/arXiv.alggeom/9711011
 arXiv:
 arXiv:alggeom/9711011
 Bibcode:
 1997alg.geom.11011K
 Keywords:

 Algebraic Geometry;
 Mathematics  Algebraic Geometry
 EPrint:
 plain TEX, 43 pages. Final version, to appear in Proceedings of the Taniguchi Symposium "Algebraic geometry and integrable systems" (KobeKyoto, July 1997)