Consecutive Patterns, Kostant's Problem and Type A₆

2025/03/10 by Creedon, Samuel, Mazorchuk, Volodymyr · 1 citation
Computer Science · #05E10 (Secondary) #17B10 (Primary) #Advanced Algebra and Logic #FOS: Mathematics #Logic, Reasoning, and Knowledge #Logic, programming, and type systems #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2503.07809

openalex publication_date 2025/03/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a permutation w in the symmetric group \mathfrakS_n, let L(w) denote the simple highest weight module in the principal block of the BGG category O for the Lie algebra \mathfraksl_n(ℂ). We first prove that L(w) is Kostant negative whenever w consecutively contains certain patterns. We then provide a complete answer to Kostant's problem in type A₆ and show that the indecomposability conjecture also holds in type A₆, that is, applying an indecomposable projective functor to a simple module outputs either an indecomposable module or zero.

Cited by

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

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