A Higgs bundle on a Hermitian symmetric space

Abstract

Let M : = Γ\G/K be the quotient of an irreducible Hermitian symmetric space G/K by a torsionfree cocompact lattice $${\Gamma \subset G}$$ . Let V be a complex irreducible representation of G. We give a Hodge decomposition of the cohomology of the Γ-module V in terms of the cohomologies of automorphic vector bundles on M associated to the Lie algebra cohomologies $${H*({\mathfrak p}^{+} ,V)}$$ .