STRINGS AND 2-DIMENSIONAL QCD FOR FINITE-N

The string theory description of SU(N) Yang-Mills on an arbitrary two- dimensional manifold, previously developed for the large N asymptotic expansion, is extended to include finite values of N. The theory is co nsidered from two points of view, first using a canonical Hamiltonian formulation, second using a global description of the partition functi on. In both formalisms, the effect on the string theory of taking a fi nite value of N is described by a local projection operator which has a simple description in terms of the symmetric group S-n.