TL;DR
This paper develops a diagrammatic approach to categorify the spherical module over the Hecke algebra, establishing a basis for morphism spaces and proving equivalence to an existing algebraic spherical category.
Contribution
It introduces a novel diagrammatic categorification of the spherical module over the Hecke algebra, connecting diagrammatic and algebraic frameworks.
Findings
Constructed a diagrammatic categorification of the spherical module.
Established a basis for morphism spaces in the category.
Proved the equivalence to an existing algebraic spherical category.
Abstract
We construct a diagrammatic categorification of the spherical module over the Hecke algebra. We establish a basis for the morphism spaces of this category, and prove that it is equivalent to an existing algebraic spherical category.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Algebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology