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Let X be a compact connected Riemann surface of genus g , with \(g\, \ge \,2\) , and let \(\xi \) be a holomorphic line bundle on X with \(\xi ^{\otimes 2}\,=\, {\mathcal O}_X\) . Fix a theta characteristic \({\mathbb {L}}\) on X . Let \({\mathcal M}_X(r,\xi )\) be the moduli space of stable vector bundles E on X of rank r such that \(\bigwedge ^r E\,=\, \xi \) and \(H^0(X,\, E\otimes {\mathbb L})\,=\, 0\) . Consider the quotient of \({\mathcal M}_X(r,\xi )\) by the involution given by \(E\, \longmapsto \, E^*\) . We construct an algebraic morphism from this quotient to the moduli space of \(\textrm{SL}(r,{\mathbb C})\) opers on X . Since \(\dim {\mathcal M}_X(r,\xi )\) coincides with the dimension of the moduli space of \(\textrm{SL}(r,{\mathbb C})\) opers, it is natural to ask about the injectivity and surjectivity of this map.
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