North-Holland A BRST analysis of W-symmetries

We perform a classical BRST analysis of the symmetries corresponding to a generic w~-alge-bra. An essential feature of our method is that we write the wy-algebra in a special basis such that the algebra manifestly has a “nested ” set of subalgebras u~C v~’~c... C vi,, WN where the subalgebra v~,r(i 2 N) consists of generators of spin s {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. 1