2.00 p.m. - 3.00 p.m.
A Wonderful Embedding of the Loop Group
Pablo Solis
Berkeley, US.
15-03-13

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Abstract

The wonderful compactification of a semi simple adjoint group is a smooth projective variety with boundary given by a normal crossing divisor. It was constructed in 1983 by De Concini and Procesi and plays an important role in the theory of spherical varieties. In this talk I will discuss a generalization of this result to the group $LG$ of loop in a semisimple group (or more accurately to the semi direct product $\mathbb{C}^\times \ltimes LG$). The construction utilizes the representation theory of Kac-Moody groups and produces an embedding in a manner equivariant for the left and right of action of the group. The loop group analogue is suggested by work of Faltings in relation to the compactification of moduli of G-bundles over nodal curves.