Relative hard Lefschetz for Soergel bimodules

Ben Elias; Geordie Williamson

Relative hard Lefschetz for Soergel bimodules

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arxiv 1607.03271 v2 pith:2ISLH35R submitted 2016-07-12 math.RT math.AGmath.QA

Ben Elias , Geordie Williamson This is my paper · ORCID

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We prove the relative hard Lefschetz theorem for Soergel bimodules. It follows that the structure constants of the Kazhdan-Lusztig basis are unimodal. We explain why the relative hard Lefschetz theorem implies that the tensor category associated by Lusztig to any 2-sided cell in a Coxeter group is rigid and pivotal.

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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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