Tetrahedron equations, boundary states and the hidden structure of U-q (D-n((1)))

Simple periodic 3D → 2D compactification of the tetrahedron equations gives the Yang–Baxter equations for various evaluation representations of \mathscr{U}_q(\widehat{sl}_n) . In this paper we construct an example of fixed non-periodic 3D boundary conditions producing a set of Yang–Baxter equations for \mathscr{U}_q\big(D_n^{(1)}\big) . These boundary conditions resemble a fusion in the hidden direction