Skein Modules from Skew Howe Duality and Affine Extensions
We show that we can release the rigidity of the skew Howe duality process for sln 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 slm case, corresponding to looking at tangles embed...
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| Datum: | 2015 |
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| Format: | Artikel |
| Sprache: | English |
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Інститут математики НАН України
2015
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| Schriftenreihe: | Symmetry, Integrability and Geometry: Methods and Applications |
| Online Zugang: | http://dspace.nbuv.gov.ua/handle/123456789/147018 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Skein Modules from Skew Howe Duality and Affine Extensions / H. Queffelec // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 39 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | We show that we can release the rigidity of the skew Howe duality process for sln 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 slm 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 Uq(sln) representations. The categorification proposed in a joint work with A. Lauda and D. Rose also admits a direct extension in the affine case. |
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