Extended Sugawara construction for the superalgebras SU(M+1|N+1). II. The third-order Casimir algebra

The machinery developed in paper I is used to compute the operator-product algebra (OPA) of an operator constructed from the third-order Casimir invariant of the superalgebra SU(m|n). The vertex operator construction of SU(m|n)(1) is used to find a realization of the OPA for level k=1 in terms of free bosonic fields only. It turns out that in many respects the conformal structure of the affinized Lie superalgebra SU(m|n)(1) is similar to that of the Kač-Moody algebra SU(m-n)(1). An intermediate result suggests the occurrence of extended conformal symmetries in bc systems, to which we will devote a separate discussion.