COSET REALIZATION OF UNIFYING W ALGEBRAS

We construct several quantum coset W algebras, e.g. sl(2,R)/U(1) and sl(2,R) + sl(2,R)/sl(2,R), and argue that they are finitely nonfreely generated. Furthermore, we discuss in detail their role as unifying W algebras of Casimir W algebras. We show that it is possible to give coset 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 realizations provide a generalization of level-rank duality of dual coset pairs. As further examples of finitely nonfreely generated quantum W algebras, we discuss orbifolding of W 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 W algebras probably yields infinitely nonfreely generated classical W algebras.