Chennai Mathematical Institute


2.00 p.m. - 3.00 p.m.
A Wonderful Embedding of the Loop Group

Pablo Solis
Berkeley, US.


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.