Soergel Calculus with patches
Leonardo Maltoni
TL;DR
This paper adapts the diagrammatic approach of the Hecke category to Rouquier complexes, enabling the recovery of fundamental relations and formulas in categorification of braid groups.
Contribution
It introduces a diagrammatic presentation for Rouquier complexes within the dg category framework, advancing the understanding of their algebraic relations.
Findings
Categorification of braid group relations
Recovery of Rouquier formula
Diagrammatic description of Rouquier complexes
Abstract
We adapt the diagrammatic presentation of the Hecke category to the dg category formed by the standard representatives for the Rouquier complexes. We use this description to recover basic results about these complexes, namely the categorification of the relations of the braid group and the Rouquier formula.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Algebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology