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 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 also study other factorisations for rational R-matrices in the literature and use our trigonometric R-matrix to generalise some of these results. 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). If time permits, we will also talk about some other approaches to constructing R-matrices that we considered.
The PhD seminar is a weekly seminar held on Wednesday afternoons, at 2:30-3:30pm, for PhD students to talk about their thesis work or other projects.
There is tea in the common room afterwards.