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This article is cited in 6 scientific papers (total in 6 papers)
Skein Modules from Skew Howe Duality and Affine Extensions
Hoel Queffelec Mathematical Sciences Institute, The Australian National University,
J.D. 27 Union Lane, Acton ACT 2601, Australia
Abstract:
We show that we can release the rigidity of the skew Howe duality process for $\mathfrak{sl}_n$ knot invariants by rescaling the quantum Weyl group action, and recover skein modules for web-tangles. This skew Howe duality phenomenon can be extended to the affine $\mathfrak{sl}_m$ case, corresponding to looking at tangles embedded in a solid torus. We investigate the relations between the invariants constructed by evaluation representations (and affinization of them) and usual skein modules, and give tools for interpretations of annular skein modules as sub-algebras of intertwiners for particular $U_q(\mathfrak{sl}_n)$ representations. The categorification proposed in a joint work with A. Lauda and D. Rose also admits a direct extension in the affine case.
Keywords:
skein modules; quantum groups; annulus; affine quantum groups.
Received: July 22, 2014; in final form March 30, 2015; Published online April 15, 2015
Citation:
Hoel Queffelec, “Skein Modules from Skew Howe Duality and Affine Extensions”, SIGMA, 11 (2015), 030, 36 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1011 https://www.mathnet.ru/eng/sigma/v11/p30
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Abstract page: | 129 | Full-text PDF : | 38 | References: | 39 |
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