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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 cohomological Brauer group ${\\rm Br}({\\mathcal P}{\\mathcal M}^\\alpha_s)$ is isomorphic to the cyclic group ${\\mathbb Z}/ m{\\mathbb Z}$. 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