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A Diagrammatic Temperley-Lieb Categorification

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  • Ben Elias

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.

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  • Ben Elias, 2010. "A Diagrammatic Temperley-Lieb Categorification," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2010, pages 1-47, October.
    • Handle: RePEc:hin:jijmms:530808
    DOI: 10.1155/2010/530808
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