A Diagrammatic Temperley-Lieb Categorification

Ben Elias

International Journal of Mathematics and Mathematical Sciences, 2010, vol. 2010, 1-47

Abstract:

The monoidal category of Soergel bimodules categorifies the Hecke algebra of a finite Weyl group. In the case of the symmetric group, morphisms in this category can be drawn as graphs in the plane. We define a quotient category, also given in terms of planar graphs, which categorifies the Temperley-Lieb algebra. Certain ideals appearing in this quotient are related both to the 1-skeleton of the Coxeter complex and to the topology of 2D cobordisms. We demonstrate how further subquotients of this category will categorify the irreducible modules of the Temperley-Lieb algebra.

Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:530808

DOI: 10.1155/2010/530808

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