A BRST ANALYSIS OF W-SYMMETRIES

We perform a classical BRST analysis of the symmetries corresponding to a generic w(N)-algebra. An essential feature of our method is that we write the w(N)-algebra in a special basis such that the algebra manifestly has a ''nested'' set of subalgebras v(N)N subset-of v(N)N-1 subset-of ... subset-of v(N)2 = w(N) where the subalgebra v(N)i (i = 2,..., N) consists of generators of spin s = {i, i + 1,..., N}, respectively. In the new basis the BRST charge can be written as a ''nested'' sum of N - 1 nilpotent BRST charges. In view of potential applications to (critical and/or non-critical) W-string theories we discuss the quantum extension of our results. In particular, we present the quantum BRST operator for the W4-algebra in the new basis. For both critical and non-critical W-strings we apply our results to discuss the relation with minimal models.