A Diagrammatic Temperley-Lieb Categorification
Representation Theory
2016-03-08 v2
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 cell modules of the Temperley-Lieb algebra.
Cite
@article{arxiv.1003.3416,
title = {A Diagrammatic Temperley-Lieb Categorification},
author = {Ben Elias},
journal= {arXiv preprint arXiv:1003.3416},
year = {2016}
}
Comments
long awaited update to published version