ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

7. Lie Groups and Lie Algebras

1991 MS Classification: 20, 22 Soto-Andrade, Jorge, Universidad de Chile, Santiago, Chile; Pantoja, José, Universidad Católica de Valparaiso, Chile; Vargas, Jorge, Universidad Nacional de Córdoba, Argentina. Gel’fand Models, Weil Representations and Twisted Spherical Functions A Gel’fand Model for a group G is a representation of G which contains every irreducible representation of G exactly once. We present geometrical and cohomological constructions of Gel’fand Models for some finite groups of Lie type. We also give a geometric construction of Weil representations for the SL_{∗}(2, A) groups over an involution ring (A, ∗). Finally we provide an explicit description, à la Curtis, of the spherical functions associated to the twisted finite analogue of Poincaré’s Upper Half Plane. Part of these results is also joint work with M. F. Yañez.