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Loop Groups and Parahoric Bundles on Curves

Pablo Solis (UC Berkeley)
Fredag, 14 september, 2012, at 13:15-14:15, in 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.
Organiseret af: QGM
Kontaktperson: Jørgen Ellegaard Andersen