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Seminar: Loop Groups and Parahoric Bundles on Curves

Speaker: Pablo Solis (UC Berkeley)

2012.09.20 | Christine Dilling

Date Fri 14 Sep
Time 13:15 14:15
Location Aud. D4 (1531-219)


I describe the wonderful compactification of loop groups. These compactifications are obtained by adding normal-crossing boundary divisors to the group LG of loops in a reductive group $G$ (or more accurately, to the semi-direct product $C^*  \times LG$) in a manner equivariant for the left and right $C^*  \times LG$-actions. The analogue for a torus group $T$ is the theory of toric varieties; for an adjoint group $G$, this is the wonderful compactications of De Concini and Procesi. The loop group analogue is suggested by work of Faltings in relation to the compacti cation of moduli of $G$-bundles over nodal curves. Using the loop analogue one can construct a 'wonderful' completion of the moduli stack of $G$-bundles over nodal curves which parametrizes Parahoric bundles.

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