Timothée Marquis (Université Catholique de Louvain) will speak in the geometry seminar on the 14th November. The talk will take place in the Salle de Profs (9th floor, NO) at 14.45pm. His title is “On continuous one-parameter subgroups of Kac-Moody groups” and the abstract is below.
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.