Chen–Ruan cohomology and moduli spaces of parabolic bundles over a Riemann surface

Abstract

Let $(X,\,D)$ be an m-pointed compact Riemann surface of genus at least 2. For each $x \,\in \, D$, fix full flag and concentrated weight system $\alpha$. Let $P \mathcal {M}_{\xi }$ denote the moduli space of semi-stable parabolic vector bundles of rank r and determinant $\xi$ over X with weight system $\alpha$, where r is a prime number and $\xi$ is a holomorphic line bundle over X of degree d which is not a multiple of r. We compute the Chen–Ruan cohomology of the orbifold for the action on $P \mathcal {M}_{\xi }$ of the group of r-torsion points in $\mathrm{Pic}^0(X)$.