The Hecke Bicategory

Details The Hecke Bicategory The Hecke Bicategory

2010-07-12

arxiv.org/abs/1007.1931v2

Mathematics

Quantum Algebra

27 pages, 11 .eps figures, Major revision of exposition

Scientific paper

We present an application of the program of groupoidification leading up to a sketch of a categorification of the Hecke algebroid --- the category of permutation representations of a finite group. As an immediate consequence, we obtain a categorification of the Hecke algebra. We suggest an explicit connection to new higher isomorphisms arising from incidence geometries, which are solutions of the Zamolodchikov tetrahedron equation. This paper is expository in style and is meant as a companion to Higher Dimensional Algebra VII: Groupoidification and an exploration of structures arising in the work in progress, Higher Dimensional Algebra VIII: The Hecke Bicategory, which introduces the Hecke bicategory in detail.

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