Kostant's problem for fully commutative permutations

2022/05/18 by Marco Mackaay, Mackaay, Marco, Volodymyr Mazorchuk +3 · 1 citation
Mathematics · #Algebraic structures and combinatorial models #Advanced Topics in Algebra #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.2205.09090

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.

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• Hecke combinatorics, Kåhrström's conditions and Kostant's problem

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