A skein relation for singular Soergel bimodules
Quantum Algebra
2021-07-20 v1 Geometric Topology
Representation Theory
Abstract
We study the skein relation that governs the HOMFLYPT invariant of links colored by one-column Young diagrams. Our main result is a categorification of this colored skein relation. This takes the form of a homotopy equivalence between two one-sided twisted complexes constructed from Rickard complexes of singular Soergel bimodules associated to braided webs. Along the way, we prove a conjecture of Beliakova--Habiro relating the colored 2-strand full twist complex with the categorical ribbon element for quantum .
Cite
@article{arxiv.2107.08117,
title = {A skein relation for singular Soergel bimodules},
author = {Matthew Hogancamp and David E. V. Rose and Paul Wedrich},
journal= {arXiv preprint arXiv:2107.08117},
year = {2021}
}
Comments
34 pages, many diagrams