Existence and rotatability of the twocolored JonesWenzl projector
Abstract
The twocolored TemperleyLieb algebra $2\mathrm{TL}_R({}_s {n})$ is a generalization of the TemperleyLieb algebra. The analogous twocolored JonesWenzl projector $\mathrm{JW}_R({}_s {n}) \in 2\mathrm{TL}_R({}_s {n})$ plays an important role in the EliasWilliamson construction of the diagrammatic Hecke category. We give conditions for the existence and rotatability of $\mathrm{JW}_R({}_s {n})$ in terms of the invertibility and vanishing of certain twocolored quantum binomial coefficients. As a consequence, we prove that Abe's category of Soergel bimodules is equivalent to the diagrammatic Hecke category in complete generality.
 Publication:

arXiv eprints
 Pub Date:
 February 2023
 DOI:
 10.48550/arXiv.2302.14476
 arXiv:
 arXiv:2302.14476
 Bibcode:
 2023arXiv230214476H
 Keywords:

 Mathematics  Representation Theory;
 Mathematics  Quantum Algebra
 EPrint:
 16 pages, many figures, best viewed in color