Models for the Basic Irreducible Representation of a Heisenberg Group

This talk is based on a collaboration with V. S. Varadarajan. - We study various models for the unique irreducible (and basic) representation of the Heisenberg group H associated with a locally compact group G and a multiplier m on G. Each maximal isotropic subgroup of G gives rise to a basic irreducible representa tion of H, thus one can obtain various kinds of information about the same irreducible representation by varying the subgroup. Special attention is given to the case where G arises as a Weyl system basedon the p-adic numbers.