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Towards combinatorial invariance for Kazhdan-Lusztig polynomials

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arxiv 2111.15161 v1 pith:K57W47XA submitted 2021-11-30 math.RT

Charles Blundell , Lars Buesing , Alex Davies , Petar Veličković , Geordie Williamson This is my paper · ORCID
classification math.RT
keywords combinatorialconjecturegroupsinvariancekazhdan-lusztigpolynomialssymmetricapproach
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Kazhdan-Lusztig polynomials are important and mysterious objects in representation theory. Here we present a new formula for their computation for symmetric groups based on the Bruhat graph. Our approach suggests a solution to the combinatorial invariance conjecture for symmetric groups, a well-known conjecture formulated by Lusztig and Dyer in the 1980s.

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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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