The Hecke Bicategory

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 conn...

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Bibliographic Details
Published in:Axioms 2012-12, Vol.1 (3), p.291-323
Main Author: Hoffnung, Alexander E.
Format: Article
Language:English
Subjects:
buildings
categorification
enriched bicategories
groupoidification
Hecke algebras
incidence geometries
spans
Yang–Baxter equations
Zamalodchikov tetrahedron equations
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Summary: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.
ISSN:2075-1680
2075-1680
DOI:10.3390/axioms1030291