Kostant's problem for fully commutative permutations

Abstract: Kostant's problem is a well-known problem in the representation theory of complex semi-simple finite-dimensional Lie algebras, defined and popularized by Joseph in a famous paper from 1980. It asks for which simple modules L of such a Lie algebra g the universal enveloping algebra U(g) surjects onto the space of adjointly finite linear endomorphisms of L. If L is finite-dimensional, the answer follows from the Artin-Wedderburn theorem, but if L is infinite-dimensional, the answer is not known in general. In my talk, I will explain what the answer is for a natural class of simple modules of the special linear Lie algebra sl(n) which are indexed by fully commutative permutations. This is joint work with Volodymyr Mazorchuk and Vanessa Miemietz.

Mathematics

Audience: researchers in the topic

ANTLR seminar

Series comments: This is the Algebra, Number Theory, Logic and Representation theory seminar.