  We give a rigorous calculation of the large N limit of the partition function
of SU(N) gauge theory on a 2D cylinder in the case where one boundary holomony
is a so-called special element of type $\rho$. By MacDonald's identity, the
partition function factors in this case as a product over positive roots and it
is straightforward to calculate the large N asymptotics of the free energy. We
obtain the unexpected result that the free energy in these cases is asymptotic
to N times a functional of the limit densities of eigenvalues of the boundary
holonomies. This appears to contradict the predictions of Gross-Matysin and
Kazakov-Wynter that the free energy should have a limit governed by the complex
Burgers equation.
