Brauer group of a moduli space of parabolic vector bundles over a curve

Let PMs alpha be a moduli space of stable parabolic vector bundles of rank n >= 2 and fixed determinant of degree d over a compact connected Riemann surface X of genus g(X) >= 2. If g(X) = 2, then we assume that n > 2. Let m denote the greatest common divisor of d, n and the dimensions of all the successive quotients of the quasi-parabolic filtrations. We prove that the Brauer group Br(PMs alpha) is isomorphic to the cyclic group Z/mZ. We also show that Br(PMs alpha) is generated by the Brauer class of the Brauer-Severi variety over PMs alpha obtained by restricting the universal projective bundle over X x PMs alpha.