Annular Khovanov homology and knotted Schur–Weyl representations
2017 ◽
Vol 154
(3)
◽
pp. 459-502
◽
Keyword(s):
Let $\mathbb{L}\subset A\times I$ be a link in a thickened annulus. We show that its sutured annular Khovanov homology carries an action of $\mathfrak{sl}_{2}(\wedge )$, the exterior current algebra of $\mathfrak{sl}_{2}$. When $\mathbb{L}$ is an $m$-framed $n$-cable of a knot $K\subset S^{3}$, its sutured annular Khovanov homology carries a commuting action of the symmetric group $\mathfrak{S}_{n}$. One therefore obtains a ‘knotted’ Schur–Weyl representation that agrees with classical $\mathfrak{sl}_{2}$ Schur–Weyl duality when $K$ is the Seifert-framed unknot.
2016 ◽
Vol 09
(01)
◽
pp. 1650006
Keyword(s):
1968 ◽
Keyword(s):
2020 ◽
Vol 2020
(769)
◽
pp. 87-119
Keyword(s):
Keyword(s):