  Following some motivating comments on large N two-dimensional Yang-Mills
theory, we discuss techniques for large N group representation theory, using
quantum mechanics on the group manifold U(N), its equivalence to a
quasirelativistic two-dimensional free fermion theory, and bosonization. As
applications, we compute the free energy for two-dimensional Yang-Mills theory
on the torus to O(1/N^2), and an interesting approximation to the leading
answer for the sphere. We discuss the question of whether the free energy for
the torus has R -> 1/R invariance. A substantially revised version of
hep-th/9303159 with many new results.
