Identification of the one-mode quadratic Heisenberg group with the projective group PSU(1,1) and holomorphic representation

Abstract

In this paper, we provide a new reformulation of the quadratic analogue of the Weyl relations. Especially, we offer some adjustments [10] on these relations and the corresponding group law, i.e., the quadratic Heisenberg group law. We provide a much more transparent description of the underlying manifold and we give a connection with the projective group PSU(1,1). Finally, we deduce such a holomorphic realization of the quadratic Heisenberg group.