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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| Дата: | 2015 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2015
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | 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 |
| 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| id |
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irk-123456789-1470182019-02-13T01:24:48Z Skein Modules from Skew Howe Duality and Affine Extensions Queffelec, H. 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. 2015 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/147018 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Queffelec, H. |
| spellingShingle |
Queffelec, H. Skein Modules from Skew Howe Duality and Affine Extensions Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Queffelec, H. |
| author_sort |
Queffelec, H. |
| title |
Skein Modules from Skew Howe Duality and Affine Extensions |
| 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 |
| publisher |
Інститут математики НАН України |
| publishDate |
2015 |
| url |
http://dspace.nbuv.gov.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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT queffelech skeinmodulesfromskewhowedualityandaffineextensions |
| first_indexed |
2023-05-20T17:26:20Z |
| last_indexed |
2023-05-20T17:26:20Z |
| _version_ |
1796153295378579456 |