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 generalizing the Barbasch–Vogan theorem for Lie algebras.
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Marco Mackaay, Volodymyr Mazorchuk, Vanessa Miemietz, Kostant’s problem for fully commutative permutations. Rev. Mat. Iberoam. (2023), published online firstDOI 10.4171/RMI/1428