Algebra Seminar: Kostant's problem and Hecke algebra combinatorics

Abstract: Kostant's problem is a classical problem in Lie theory which asks, for a given module M of a Lie algebra g, whether the universal enveloping algebra of g surjects onto the space of ad-finite endomorphisms of M. Under a certain specialisation, a thoerem of Ko, Mazorchuk, and Mrden, gives an equivalent reformulation of Kostant's problem which explicitly connects it to the combinatorics of Hecke algebras. In this talk I will summarise different ways we have been able to exploit this connection to obtain new results regarding Kostant's problem, the combinatorics of Hecke algebras, and related conjectures, particular in Type A. This work was done jointly with Volodymyr Mazorchuk.

The seminar will be held via Zoom link (meeting ID: 645 5572 6999, please contact the organiser for passcode)

This is a seminar in our algebra seminar series.