I am looking for the Picard group of the moduli space of semistable rank 2 parabolic vector bundles over smooth complex projective curves with trivial determinant.
Having determinant trivial, I believe we can consider the bundles as parabolic $SL(n,\mathbb{C})$-bundles as well. The closest result have found in this regard is a paper by Laszlo and Sorger, 'The line bundles on the moduli of G-bundles on a curve', but they only talk about quasi-parabolic bundles rather than parabolic bundles.
My question is: Is the picard group known already? Does anyone know of any reference? I need it urgently if possible. Any help would be appreciable.
