Abstract : Consider the moduli space M of meromorphic connections on the
trivial rank n bundle over the Riemann sphere with semisimple regular
residues. In this talk I will explain how to interpret the structure
coefficients of the character ring of GL_n(q) in terms of the action of
the symmetric groups on the cohomology of M. I will also discuss the
case of the finite unitary group. This is partly joint with F.
V. Roubtsov, V. Golyshev