On solutions to the Yang-Baxter equation related to sl(n)

by Gary Bosnjak (UCL)

Location: CYCL04, Louvain-la-Neuve
Time: Wednesday October 3, 2018 at 15:00

In this talk we consider the problem of constructing solutions to the Yang-Baxter equation. Such solutions are known as R-matrices and we study a certain class of these related to quantum affine sl(n). Using a 3D integrable model approach we derive an explicit formula for the matrix elements in the case of symmetric tensor representations with arbitrary weights. We detail the structure of this solution, including its symmetries and a factorisation in terms of more elementary R-matrices without the difference property. We link this factorisation to recent developments in stochastic exclusion processes and prove that our R-matrix can be stochastic.

We compare our results to other constructions in the literature and further clarify the composite nature of our newly obtained R-matrix. We also consider the general problem of arbitrary highest weight representations and present some results related to factorisation and stochasticity in the case of sl(3).