Tetrahedron equations, boundary states and hidden structure of U_q(D_n^1)

TL;DR

This paper explores how specific boundary conditions in 3D tetrahedron equations lead to new Yang-Baxter equations for quantum affine algebra U_q(D_n^1), revealing hidden structural connections.

Contribution

It introduces a novel non-periodic boundary condition in 3D tetrahedron equations that produces Yang-Baxter equations for U_q(D_n^1), uncovering hidden algebraic structures.

Findings

Boundary conditions produce Yang-Baxter equations for U_q(D_n^1)

Reveals hidden fusion-like structure in boundary conditions

Connects 3D tetrahedron equations to 2D integrable models

Abstract

Simple periodic 3d->2d compactification of the tetrahedron equations gives the Yang-Baxter equations for various evaluation representations of U_q(sl_n). In this paper we construct an example of fixed non-periodic 3d boundary conditions producing a set of Yang-Baxter equations for U_q(D_n^1). These boundary conditions resemble a fusion in hidden direction.