Involutions on moduli spaces and refinements of the Verlinde formula (Q1298175)

The paper studies certain involutions on the moduli-space of rank-2-bundles (of fixed determinant) on a curve. These involutions are tensor products with line-bundles of order two. One main result concerns the structure of the group generated by these involutions, proved via a detailed study of their fixed-points. The other result computes the character of the representation of this group on global sections of a power of the natural ample bundle on moduli-space. The dimension of this space is given by the Verlinde formula, and the traces of the involutions by fixed-point computations. Finally it is observed that these numbers coincide with certain invariants in topological quantum field theories.