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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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2015 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2015
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/147018 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862706952113487872 |
|---|---|
| author | Queffelec, H. |
| author_facet | Queffelec, H. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
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| first_indexed | 2025-12-07T17:02:19Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147018 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T17:02:19Z |
| publishDate | 2015 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | 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 |
| spellingShingle | Skein Modules from Skew Howe Duality and Affine Extensions Queffelec, H. |
| title | 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_short | Skein Modules from Skew Howe Duality and Affine Extensions |
| title_sort | skein modules from skew howe duality and affine extensions |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147018 |
| work_keys_str_mv | AT queffelech skeinmodulesfromskewhowedualityandaffineextensions |