AbstractIn the talk, l shall present our joint paper with A.Gerasimov and D.Lebedev. in this paper, wedevelop a representation theory approach to the study of generalized hypergeometric functions ofGelfand, Kapranov and Zelevisnky (GKZ). We show that the GKZ hypergeometric functions may beidentified with matrix elements of non-reductive Lie algebras L(N) of oscillator type. The Whittakerfunctio...
Abstract:Some Shimura varieties can be interpreted as moduli spaces of curves. In such cases this can be used to get information about modular forms. We discuss a ball quotient related to moduli of curves of genus three. We study cohomology of local systems and calculate the traces of Hecke operators by counting points on curves over finite fields. We also construct all vector-valued Picard mo...