Annular Khovanov homology and knotted Schur-Weyl representations
Geometric Topology
2019-02-20 v1 Quantum Algebra
Representation Theory
Abstract
Let L be a link in a thickened annulus. We show that its sutured annular Khovanov homology carries an action of the exterior current algebra of the Lie algebra sl_2. When L is an m-framed n-cable of a knot K in the three-sphere, its sutured annular Khovanov homology carries a commuting action of the symmetric group S_n. One therefore obtains a "knotted" Schur-Weyl representation that agrees with classical sl_2 Schur-Weyl duality when K is the Seifert-framed unknot.
Keywords
Cite
@article{arxiv.1505.04386,
title = {Annular Khovanov homology and knotted Schur-Weyl representations},
author = {J. Elisenda Grigsby and Anthony M. Licata and Stephan M. Wehrli},
journal= {arXiv preprint arXiv:1505.04386},
year = {2019}
}
Comments
38 pages, 8 figures