IJPAM: Volume 14, No. 1 (2004)

HECKE OPERATORS ON MIXED AUTOMORPHIC
FORMS AND KUGA FIBER VARIETIES

Min Ho Lee
Department of Mathematics
University of Northern Iowa
Cedar Falls, IA 50614, USA
e-mail: lee@math.uni.edu


Abstract.We discuss Hecke operators acting on the space of mixed automorphic forms and on the cohomology of families of Abelian varieties, known as Kuga fiber varieties, parametrized by an arithmetic quotient of a symmetric space associated to a real reductive group. There is a correspondence between a certain class of mixed automorphic forms and the cohomology of a Kuga fiber variety. We prove that the two types of Hecke operator actions are compatible with respect to such a correspondence.

Received: March 8, 2004

AMS Subject Classification: 11F55, 11F70, 11F60, 14K10

Key Words and Phrases: Hecke operators, automorphic forms, Kuga fiber varieties, arithmetic varieties

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2004
Volume: 14
Issue: 1