Kostant's problem for fully commutative permutations

TL;DR

This paper provides a comprehensive combinatorial solution to Kostant's problem for certain modules associated with fully commutative permutations and extends the theory to bicategories, generalizing existing theorems.

Contribution

It offers a complete combinatorial characterization for Kostant's problem in the context of fully commutative permutations and introduces a reformulation within fiab bicategories.

Findings

Complete combinatorial solution to Kostant's problem for fully commutative permutations

Reformulation of Kostant's problem in fiab bicategories

Classification of annihilators of simple objects in principal birepresentations

Abstract

We give a complete combinatorial answer to Kostant's problem for simple highest weight modules indexed by fully commutative permutations. We also propose a reformulation of Kostant's problem in the context of fiab bicategories and classify annihilators of simple objects in the principal birepresentations of such bicategories generalising the Barbasch--Vogan theorem for Lie algebras.