Brauer groups and Picard groups of the moduli of parabolic vector bundles on a nodal curve

We determine the Brauer groups and Picard groups of the moduli space U-L,U-par's par of stable parabolic vector bundles of rank r with determinant L on a complex nodal curve Y of arithmetic genus g >= 2. We also compute the Picard group of the moduli stack for parabolic SL(r)-bundles on Y and use it to give another description of the Picard group of U-L,U-par's. For g >= 2, we determine the Brauer group of the moduli space U-L's of stable vector bundles on Y of rank r with determinant L, deduce that U-L's is simply connected and show the non-existence of the universal bundle on U-L's x Y in the non-coprime case.