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Type II1 Von Neumann representations for Hecke operators on Maass forms and inequalities for their eigenvalues
by
Florin Radulescu
University of Rome and IMAR
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 on Maass forms. These inequalities are the consequence of a "double" action of the Hecke algebra which can be seen only in the type II1 representation. The classical Hecke operators are then a "diagonal" of this double action.
Date received: June 11, 2008
Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cawh-85.