In a previous paper [J. Combin. Theory Ser. A, 2019], the author constructed geometric crystal on variety Xk:=Gr(k,n)×C× which tropicalizes to affine structure rectangular tableaux with n−k rows. this sequel, we define and study R-matrix, birational map R:Xk1×Xk2→Xk2×Xk1 combinatorial R-matrix pairs of tableaux. We show that R is an isomorphism crystals, it satisfies Yang–Baxter relation. case ...

Abstract In recent years, new properties of space-time duality in the Hamiltonian formalism certain integrable classical field theories have been discovered and led to their reformulation using ideas from covariant theory: this sense, nature r -matrix structure was unravelled. Here, we solve open question extending these results a whole hierarchy. We choose Ablowitz–Kaup–Newell–Segur (AKNS) To ...