Speaker
Olivier Guichard
(Université de Strasbourg)
Description
The principal sl_2 is an object of importance in the understanding of the
structure of simple Lie algebras.
In this talk we will address the question when an irreducible subalgebra
contains the semisimple element of a principal sl_2 and give a classification
result for those subalgebras. We will also explain the motivation of that
question coming from Higgs bundles and representations of fundamental groups of
Kähler manifolds.
The classifcation is based of the understanding of "teeny-weeny"
representations of a Lie algebra, i.e. representations all of whom nonzero
weight spaces are one dimensional. We will also give a classification result
for those representations.
