COSET REALIZATION OF UNIFYING W ALGEBRAS

We construct several quantum coset W algebras, e.g. sl(2,R)/U(1) and s l(2,R) + sl(2,R)/sl(2,R), and argue that they are finitely nonfreely g enerated. Furthermore, we discuss in detail their role as unifying W a lgebras of Casimir W algebras. We show that it is possible to give cos et realizations of various types of unifying W algebras; for example, the diagonal cosets based on the sympletic Lie algebras sp(2n) realize the unifying W algebras which have previously been introduced as WD(- n). In addition, minimal models of WD(-n) are studied. The coset reali zations provide a generalization of level-rank duality of dual coset p airs. As further examples of finitely nonfreely generated quantum W al gebras, we discuss orbifolding of W algebras which on the quantum leve l 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 W algebras p robably yields infinitely nonfreely generated classical W algebras.