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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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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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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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/147018 |
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| 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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Queffelec, H. 2019-02-12T20:58:58Z 2019-02-12T20:58:58Z 2015 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. 1815-0659 2010 Mathematics Subject Classification: 81R50; 17B37; 17B67; 57M25; 57M27 DOI:10.3842/SIGMA.2015.030 https://nasplib.isofts.kiev.ua/handle/123456789/147018 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. This paper is a contribution to the Special Issue on New Directions in Lie Theory. The full collection is available at http://www.emis.de/journals/SIGMA/LieTheory2014.html. I would like to thank my advisors Christian Blanchet and Catharina Stroppel for their constant support, and Aaron Lauda for his great help. Many thanks also to David Rose, Peng Shan, Pedro Vaz and Emmanuel Wagner for all useful discussions we had, Marco Mackaay for pointing out the interest of the af fine Hecke algebra, and especially to Mathieu Mansuy for teaching me everything I know about af fine algebras. I also wish to acknowledge the great help of the anonymous referees. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Skein Modules from Skew Howe Duality and Affine Extensions Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Skein Modules from Skew Howe Duality and Affine Extensions |
| spellingShingle |
Skein Modules from Skew Howe Duality and Affine Extensions Queffelec, H. |
| title_short |
Skein Modules from Skew Howe Duality and Affine Extensions |
| title_full |
Skein Modules from Skew Howe Duality and Affine Extensions |
| title_fullStr |
Skein Modules from Skew Howe Duality and Affine Extensions |
| title_full_unstemmed |
Skein Modules from Skew Howe Duality and Affine Extensions |
| title_sort |
skein modules from skew howe duality and affine extensions |
| author |
Queffelec, H. |
| author_facet |
Queffelec, H. |
| publishDate |
2015 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
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.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/147018 |
| citation_txt |
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. |
| work_keys_str_mv |
AT queffelech skeinmodulesfromskewhowedualityandaffineextensions |
| first_indexed |
2025-12-07T17:02:19Z |
| last_indexed |
2025-12-07T17:02:19Z |
| _version_ |
1850869745840029696 |