The Hodge theory of Soergel bimodules

Ben Elias; Geordie Williamson

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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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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