Nilpotent orbits and the Yang-Baxter Equation

Paul Zinn-Justin


We discuss the connection between Joseph's theory of orbital varieties and of their multidegrees (i.e. equivariant cohomology) and some rational solutions of the Yang-Baxter equation. We detail the construction in the case of matrices that square to zero, and how we are led to a degeneration of the Brauer algebra. We explain the relation to earlier work by Fomin and Kirillov on double Schubert polynomials, and to the recently introduced Brauer loop scheme.