THE COMPLETE COHOMOLOGY OF THE W(3) STRING

We present a simple procedure for constructing the complete cohomology of the BRST operator of the two-scalar and multi-scalar W3 strings. T he method consists of obtaining two level-15 physical operators in the two-scalar W3 string that are invertible, and that can normal order w ith all other physical operators. They can be used to map all physical operators into non-trivial physical operators whose momenta lie in a fundamental unit cell. By carrying out an exhaustive analysis of physi cal operators in this cell, the entire cohomology problem is solved.