Journal of the
Korean Mathematical Society JKMS

In this paper, we introduce the Fock representation $U^{F,\M}$ of the Heisenberg group $H_{\BR}^{(g,h)}$ associated with a positive definite symmetric half-integral matrix ${\Cal M}$ of degree $h$ and prove that $U^{F,\M}$ is unitarily equivalent to the Schr{\"o}dinger representation of index $\M$.

Keywords: Heisenberg groups, Schr{\"o}dinger representations, Fock representations

MSC numbers: Primary 22E25, 22E27