On Lusztig's Conjecture
by Paul Sobaje
Abstract: Let G be a reductive algebraic group over an algebraically closed field of characteristic \(p>0\). An important problem in modular representation theory is computing the characters of simple rational G-modules. In this talk we will give an introduction to Lusztig's conjecture, specifically showing how it addresses the previously stated problem. We will then give an overview of the current status of this conjecture, highlighting some of the main approaches toward proving it.