Localized calculus for the Hecke category

Ben Elias; Geordie Williamson

Localized calculus for the Hecke category

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arxiv 2011.05432 v2 pith:6STAVCQP submitted 2020-11-10 math.RT

Ben Elias , Geordie Williamson This is my paper · ORCID

classification math.RT

keywords categoryheckefunctorlocalizationabstractauthorsbimodulesbuilt

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We construct a functor from the Hecke category to a groupoid built from the underlying Coxeter group. This fixes a gap in an earlier work of the authors. This functor provides an abstract realization of the localization of the Hecke category at the field of fractions. Knowing explicit formulas for the localization is a key technical tool in software for computations with Soergel bimodules.

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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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