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Tetrahedron equations, boundary states and hidden structure of Uq(Dn1)

Abstract

Simple periodic 3d->2d compactification of the tetrahedron equations gives the Yang-Baxter equations for various evaluation representations of Uq(sln). In this paper we construct an example of fixed non-periodic 3d boundary conditions producing a set of Yang-Baxter equations for Uq(Dn1). These boundary conditions resemble a fusion in hidden direction.

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