Handlebody diagram algebras
Quantum Algebra
2023-08-17 v3 Geometric Topology
Representation Theory
Abstract
In this paper we study handlebody versions of some classical diagram algebras, most prominently, handlebody versions of Temperley-Lieb, blob, Brauer, BMW, Hecke and Ariki-Koike algebras. Moreover, motivated by Green-Kazhdan-Lusztig's theory of cells, we reformulate the notion of (sandwich, inflated or affine) cellular algebras. We explain this reformulation and how all of the above algebras are part of this theory.
Cite
@article{arxiv.2105.07049,
title = {Handlebody diagram algebras},
author = {Daniel Tubbenhauer and Pedro Vaz},
journal= {arXiv preprint arXiv:2105.07049},
year = {2023}
}
Comments
45 pages, lots of figures, revision following referees comments, to appear in Rev. Mat. Iberoam, comments welcome