COSET REALIZATION OF UNIFYING ${\mathcal W}$ ALGEBRAS

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Abstract
We construct several quantum coset algebras, e.g. and and argue that they are finitely nonfreely generated. Furthermore, we discuss in detail their role as unifying algebras of Casimir algebras. We show that it is possible to give coset realizations of various types of unifying algebras; for example, the diagonal cosets based on the symplectic Lie algebras sp(2n) realize the unifying algebras which have previously been introduced as . In addition, minimal models of are studied. The coset realizations provide a generalization of level-rank duality of dual coset pairs. As further examples of finitely nonfreely generated quantum algebras, we discuss orbifolding of algebras which on the quantum level has different properties than in the classical case. We demonstrate through some examples that the classical limit — according to Bowcock and Watts — of these finitely nonfreely generated quantum algebras probably yields infinitely nonfreely generated classical algebras.

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