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Our aim here is to compute the holomorphic automorphism group of ${\\mathcal Q}_X(r,d_p,d_z)$. It is shown that the connected component of $\\text{Aut}( {\\mathcal Q}_X(r,d_p,d_z))$ containing the identity automorphism is $\\text{PGL}(r,{\\mathbb C})$. 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