In this paper we compute in some new cases the cardinalities of fibers certain natural fibrations that appear analysis configuration space Heisenberg ring. This is done by means cyclic group actions on subsets restricted partitions.

We describe the extremal positive harmonic functions for finitely supported measures on discrete Heisenberg group: they are proportional either to characters or translates of induced from characters.

We perform a generalised Scherk-Schwarz reduction of the effective action of the het-erotic string on T 6 to obtain a massive N = 4 supergravity theory in four dimensions. The local symmetry-group of the resulting d = 4 theory includes a Heisenberg group, which is a subgroup of the global O(6, 6 + n) obtained in the standard reduction. We show explicitly that the same theory can be obtained by ...