ALGB Seminar: Timothée Marquis, Louvain-La-Neuve

Title: On continuous one-parameter subgroups of Kac-Moody groups
 

Abstract:
Kac-Moody groups may be viewed as infinite dimensional generalisations of (finite-dimensional) Lie groups: one starts with a (usually infinite dimensional) Lie algebra - a so-called Kac-Moody algebra - and then one "exponentiates" this Lie algebra in some way to get a group functor over the category of Z-algebras. A Kac-Moody group G is then by definition the evaluation of such a functor over a field. Over R or C, the group G can be equipped with a topology coming from the field, which turns it into a topological group. It is then natural to ask for such a G whether one can reconstruct, as in the classical (finite-dimensional) case, the Lie algebra from the topological group structure of G. This suggests to determine the set of topological one-parameter subgroups of G. In this talk, I will explain how this can be achieved, using the natural actions of Kac-Moody groups on some geometric objects called buildings. No special prerequisites are required.