1307.6808 (L. Poulain d'Andecy)

Fusion procedure for the Yang-Baxter equation and Schur-Weyl duality    [PDF]

L. Poulain d'Andecy

We first review the fusion procedure for an arbitrary solution of the Yang-Baxter equation and the study of distinguished invariant subspaces for the fused solutions. Then we apply these general results to four particular solutions: the Yang solution, its standard deformation and their generalizations for super vector spaces. For the Yang solution, respectively, its "super" generalization, we explain how, using the fusion formula for the symmetric group together with the (super) Schur-Weyl duality, the fusion procedure allows to construct a family of fused solutions of the Yang-Baxter equation acting on irreducible representations of the general linear Lie algebra, respectively, of the general linear Lie superalgebra. For the deformations of the two previous solutions, we use the fusion formula for the Hecke algebra together with the (super) quantum Schur--Weyl duality to obtain fused solutions acting on irreducible representations of the quantum groups associated to the general linear Lie (super)algebras.

View original: http://arxiv.org/abs/1307.6808