Type Ii1 Von Neumann Representations for Hecke Operators on Maass Forms and Ramanujan-peterson Conjecture


We prove that classical Hecke operators on Maass forms are a special case of completely positive maps on II1 factors, associated to a pair of isomorphic subfactors. This representation induces several matrix inequalities on the eigenvalues of the Hecke operators Maass forms. In particular the family of eigenvalues corresponding to an eigenvector is a… (More)