Abstract
Let X be a compact Riemann surface of genus greater than or equal to 2.
The semistable holomorphic vector bundles on X of rank n and determinant
L are parametrised by the moduli space M(n,L). The Picard group of M(n,L)
is isomorphic to Z with a unique ample generator K(n,L). The spaces Z_k(n,L)
of holomorphic sections in the k'th tensor power of K(n,L) have been studied
intensely, due to their central role in the gauge-theoretic approach to 2+1
dimensional TQFT.
There is a natural action on M(n,L) of the group J^(n)(X) of n-torsion points
in the Jacobian of X, gotten by tensoring with the corresponding line bundles.
I define certain lifts of this action to K(n,L) (and hence to Z_k(n,L) and give
a presentation of the group generated by such lifts. In the proces, a detailed
study of the fixed point varieties for the action of J^(n)(X) on M(n,L) becomes
necessary.
Contact person:Jørgen Ellegaard Andersen.