A Diagrammatic Temperley-Lieb Categorification

الملخص EN

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.