Geodesic
Quasi-solvable lattice models for $\operatorname {Sp}_{2n}$ and $\operatorname {SO}_{2n+1}$ Demazure atoms and characters
Forum of Mathematics, Sigma, Tome 10 (2022)

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We construct coloured lattice models whose partition functions represent symplectic and odd orthogonal Demazure characters and atoms. We show that our lattice models are not solvable, but we are able to show the existence of sufficiently many solutions of the Yang–Baxter equation that allow us to compute functional equations for the corresponding partition functions. From these functional equations, we determine that the partition function of our models are the Demazure atoms and characters for the symplectic and odd orthogonal Lie groups. We coin our lattice models as quasi-solvable. We use the natural bijection of admissible states in our models with Proctor patterns to give a right key algorithm for reverse King tableaux and Sundaram tableaux. 
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     author = {Valentin Buciumas and Travis Scrimshaw},
     title = {Quasi-solvable lattice models for $\operatorname {Sp}_{2n}$ and $\operatorname {SO}_{2n+1}$ {Demazure} atoms and characters},
     journal = {Forum of Mathematics, Sigma},
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     year = {2022},
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Valentin Buciumas; Travis Scrimshaw. Quasi-solvable lattice models for $\operatorname {Sp}_{2n}$ and $\operatorname {SO}_{2n+1}$ Demazure atoms and characters. Forum of Mathematics, Sigma, Tome 10 (2022). doi: 10.1017/fms.2022.49

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