1. A Diagrammatic Temperley-Lieb Categorification.
- Author
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Elias, Ben
- Subjects
- *
MODULES (Algebra) , *CATEGORIES (Mathematics) , *BLOWING up (Algebraic geometry) , *FUNCTOR theory , *WEYL groups , *SYMMETRIC spaces , *MORPHISMS (Mathematics) - 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 irreduciblemodules of the Temperley-Lieb algebra. [ABSTRACT FROM AUTHOR]
- Published
- 2010
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