ON THE SUPER FIELD REALIZATION OF SUPER-CASIMIR ${\mathcal W} {\mathcal A} _n$ ALGEBRAS

Abstract

We give an explicit quantum super field construction of the [Formula: see text] super-Casimir [Formula: see text] algebras, which is obtained from supersymmetric Miura transformation for the Lie super-algebra [Formula: see text]. And also we give an extension of this algebras including a super-vertex operator which depends on simple root system of [Formula: see text].