Skein Modules from Skew Howe Duality and Affine Extensions

Symmetry Integrability and Geometry-Methods and Applications

article

Hoel Queffelec¹ 

[1] Mathematical Sciences Institute, The Australian National University

关键词: skein modules;    quantum groups;    annulus;    af fine quantum groups;   

DOI  :  10.3842/SIGMA.2015.030

来源: National Academy of Science of Ukraine

【 摘 要 】

We show that we can release the rigidity of the skew Howe duality process for ${\mathfrak sl}_n$ 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 ${\mathfrak sl}_m$ 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 $U_q({\mathfrak sl}_n)$ representations. The categorification proposed in a joint work with A. Lauda and D. Rose also admits a direct extension in the affine case.

【 授权许可】

Unknown