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The Hodge theory of Soergel bimodules

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arxiv 1212.0791 v2 pith:QVI7MAHA submitted 2012-12-04 math.RT

Ben Elias , Geordie Williamson This is my paper · ORCID
classification math.RT
keywords soergelbimodulesconjecturededucekazhdan-lusztigalgebraicarbitrarycharacters
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We prove Soergel's conjecture on the characters of indecomposable Soergel bimodules. We deduce that Kazhdan-Lusztig polynomials have positive coefficients for arbitrary Coxeter systems. Using results of Soergel one may deduce an algebraic proof of the Kazhdan-Lusztig conjecture.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  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.

  2. HOMFLYPT homology for links in handlebodies via type A Soergel bimodules

    math.QA 2019-08 accept novelty 7.0 of 10

    Links in genus-g handlebodies are assigned a triply-graded homology built from singular Soergel bimodules and Hochschild cohomology, generalizing colored HOMFLYPT homology.

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