Mackaay, MarcoMazorchuk, VolodymyrMiemietz, Vanessa2024-04-152024-04-1520230213-2230http://hdl.handle.net/10400.1/20632We 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 generalizing the Barbasch-Vogan theorem for Lie algebras.engKostant’s problemSimple highest weight moduleFully commutative permutationAnnihilatorBicategoryKostant’s problem for fully commutative permutationsjournal article10.4171/rmi/1428