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Subexpressions and the Bruhat order for double cosets

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arxiv 2307.15726 v2 pith:KD2CIYMM submitted 2023-07-28 math.CO math.RT

Ben Elias , Hankyung Ko , Nicolas Libedinsky , Leonardo Patimo This is my paper · ORCID
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keywords bruhatordercosetsdoublecompatibilityideallowerprove
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The Bruhat order on a Coxeter group is often described by examining subexpressions of a reduced expression. We prove that an analogous description applies to the Bruhat order on double cosets. This establishes the compatibility of the Bruhat order on double cosets with concatenation, leading to compatibility between the monoidal structure and the ideal of lower terms in the singular Hecke 2-category. We also prove other fundamental properties of this ideal of lower terms.

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  1. Idempotents, traces, and dimensions in Hecke categories

    math.RT 2025-07 conditional novelty 8.0 of 10

    The paper provides closed formulas for recursible local intersection forms and recursive partial trace formulas that reduce categorical dimensions in asymptotic Hecke categories to diagrammatic computations.

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