A Holstein-Primakoff and Dyson Realizations for the Lie Superalgebra gl(m/n+1)

Abstract

The known Holstein-Primakoff and Dyson realizations for the Lie algebras $gl(n+1),\;n=1,2,\ldots$ in terms of Bose operators are generalized to the class of the Lie superalgebras $gl(m/n+1)$ for any $n$ and $m$. Formally the expressions are the same as for $gl(m+n+1)$, however both Bose and Fermi operators are involved.