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(Co)Minuscule Hecke categories

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arxiv 2409.16131 v1 pith:K2L5MXRH submitted 2024-09-24 math.RT math.CO

Joseph Baine This is my paper · ORCID
classification math.RTmath.CO
keywords categoriesheckeminusculeantisphericalbasesbehaviourachievedcharacteristic
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We determine the p-Kazhdan-Lusztig bases for antispherical (co)minuscule Hecke categories in all characteristics, and for spherical (co)minuscule Hecke categories in good characteristic. This is achieved using geometric and diagrammatic methods. The 2-Kazhdan-Lusztig bases of antispherical cominuscule Hecke categories exhibit extremely pathological behaviour. The notions of p-small resolutions and p-tight elements are introduced and conjecturally explain this behaviour.

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  1. Big data approach to Kazhdan-Lusztig polynomials

    math.RT 2024-12 conditional novelty 6.0 of 10

    Data on Kazhdan-Lusztig polynomials up to S_11 suggests superexponential growth of extremal coefficients, near-universal unimodality, and a conjectured closed family (1+v+...+v^l)^{k-1}.

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