Quasi-solvable lattice models for and Demazure atoms and characters

Abstract We construct coloured lattice models whose partition functions represent symplectic and odd orthogonal Demazure characters atoms. show that our are not solvable, but we able to the existence of sufficiently many solutions Yang–Baxter equation allow us compute functional equations for corresponding functions. From these equations, determine function atoms Lie groups. coin as quasi-solvable. use natural bijection admissible states in with Proctor patterns give a right key algorithm reverse King tableaux Sundaram tableaux.