Revista de la Unión Matemática Argentina
Print version ISSN 0041-6932
LEE, Min Ho. Hecke operators on cohomology. Rev. Unión Mat. Argent. [online]. 2009, vol.50, n.1, pp. 99-144. ISSN 0041-6932.
Hecke operators play an important role in the theory of automorphic forms, and automorphic forms are closely linked to various cohomology groups. This paper is mostly a survey of Hecke operators acting on certain types of cohomology groups. The class of cohomology on which Hecke operators are introduced includes the group cohomology of discrete subgroups of a semisimple Lie group, the de Rham cohomology of locally symmetric spaces, and the cohomology of symmetric spaces with coefficients in a system of local groups. We construct canonical isomorphisms among such cohomology groups and discuss the compatibility of the Hecke operators with respect to those canonical isomorphisms.