Annular Khovanov homology and knotted Schur–Weyl representations
Annular Khovanov homology and knotted Schur–Weyl representations
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环形 Khovanov 同源性和打结 Schur-Weyl 表示
DOI：
10.1112/s0010437x17007540
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发表时间：
2015
影响因子：
1.8
通讯作者：
S. Wehrli
中科院分区：
文献类型：
--
作者：
J. E. Grigsby;Anthony M. Licata;S. Wehrli
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.
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.
Khovanov 模块和取消链接的检测
影响因子：
2
作者：
Hedden, Matthew;Ni, Yi
通讯作者：
Ni, Yi