The Holstein-Primakoff and Dyson realizations for the Lie superalgebra gl(m/n+1)

The known Holstein-Primakoff and Dyson realizations for gl(n + 1), n = 1,2, ..., in terms of Bose operators (Okubo S 1975 J. Math. Phys. 16 528) 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.