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Parahoric bundles and parabolic bundles

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Moduli Spaces

Let $X$ be a compact Riemann surface of genus $g geq 2$ and let $G$ be a semisimple simply connected algebraic group. We introduce the notion of a {m parahoric} $G$—bundle or equivalently a torsor under a suitable Bruhat-Tits group scheme. We also construct the moduli space of semistable parahoric $G$—bundles and identify the underlying topological space of this moduli space with certain spaces of homomorphisms of Fuchsian groups into maximal compact subgroup of $G$. These results generalize the earlier results of Mehta and Seshadri on parabolic vector bundles. (joint work with C.S Seshadri).

This talk is part of the Isaac Newton Institute Seminar Series series.

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