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Skein Modules from Skew Howe Duality and Affine Extensions
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- Symmetry, Integrability and Geometry: Methods and Applications, 2015, том 11
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Skein Modules from Skew Howe Duality and Affine Extensions
Інший ID:
2010 Mathematics Subject Classification: 81R50; 17B37; 17B67; 57M25; 57M27
DOI:10.3842/SIGMA.2015.030
DOI:10.3842/SIGMA.2015.030
Посилання:
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.
Підтримка:
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.
Дата:
2015
Переглядів:
495
Завантажень:
230
Анотація:
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.
