  We use the relation between 2d Yang-Mills and Brownian motion to show that 2d
Yang-Mills on the cylinder is related to Chern-Simons theory in a class of lens
spaces. Alternatively, this can be regarded as 2dYM computing certain
correlators in conformal field theory. We find that the partition function of
2dYM reduces to an operator of the type U=ST^pS in Chern-Simons theory for
specific values of the YM coupling but finite k and N. U is the operator from
which one obtains the partition function of Chern-Simons on S^3/Z_p, as well as
expectation values of Wilson loops. The correspondence involves the imaginary
part of the Yang-Mills coupling being a rational number and can be seen as a
generalization of the relation between Chern-Simons/WZW theories and
topological 2dYM of Witten, and Blau ant Thompson. The present reformulation
makes a number of properties of 2dYM on the cylinder explicit. In particular,
we show that the modular transformation properties of the partition function
are intimately connected with those of affine characters.
