Discrete Heisenberg-Weyl Group and modular group

Abstract

It is shown that the generators of two discrete Heisenberg-Weyl groups with irrational rotation numbers θ and -1/θ generate the whole algebra B of operators on L2(R). The natural action of the modular group in B is implied. Applications to dynamical algebras appearing in lattice regularization and some duality principles are discussed. © 1995 Kluwer Academic Publishers.