Generalized Heisenberg Groups and Self-Duality

Marco Bonatto

Università di Ferrara

In this talk we compare two generalizations of Heisenberg groups and study their connection to one of the major open problems in the field of locally compact abelian groups, namely the description of the self-dual locally compact abelian groups. The first generalization is presented by the so called generalized Heisenberg groups, defined in analogy with the classical Heisenberg group, and the second one is inspired by the construc- tion proposed by Mumford and named after him as Weyl-Mumford groups (WM groups). These two families can be defined also in the framework of topological groups. We investigate the relationship between locally compact WM groups, locally compact generalized Heisenberg groups with center isomorphic to T, and symplectic self-dualities.