A BRST ANALYSIS OF W-SYMMETRIES

We perform a classical BRST analysis of the symmetries corresponding t o a generic w(N)-algebra. An essential feature of our method is that w e write the w(N)-algebra in a special basis such that the algebra mani festly has a ''nested'' set of subalgebras v(N)N subset-of v(N)N-1 sub set-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}, respective ly. In the new basis the BRST charge can be written as a ''nested'' su m of N - 1 nilpotent BRST charges. In view of potential applications t o (critical and/or non-critical) W-string theories we discuss the quan tum extension of our results. In particular, we present the quantum BR ST 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 w ith minimal models.