### Parahoric bundles and parabolic bundles

Balaji, V *(Chennai Mathematical Institute)*

Tuesday 15 February 2011, 10:00-11:00

Seminar Room 1, Newton Institute

#### Abstract

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 {\em 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).

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