Let S be a k-punctured Riemann surface of genus g, and let C_1, ..., C_k
be
generic conjugacy
classes of GL(n,C). Then one can consider the space M of isomorphism
classes of representations
\pi_1(S ) ---> GL(n,C) where a simple loop encircling the puncture a_i
is
sent
to \bar C_i.
We are interested in the connection between the geometry of M (mixed
Hodge structures),
Macdonald symmetric functions and the representation theory of GL_n(Fq)
(e.g. multiplicities in
tensor products of characters). We will in particular discuss the case k
= g = 1.