Abstract
Abstract The tetrahedron equation introduced by Zamolodchikov is a three-dimensional generalization of the Yang–Baxter equation. Several types of solutions to the tetrahedron equation that have connections to quantum groups can be viewed as q-oscillator valued vertex models with matrix elements of the L-operators given by generators of the q-oscillator algebra acting on the Fock space. Using one of the q = 0-oscillator valued vertex models introduced by Bazhanov–Sergeev, we introduce a family of partition functions that admits an explicit algebraic presentation using Schur functions. Our construction is based on the three-dimensional realization of the Zamolodchikov–Faddeev algebra provided by Kuniba–Maruyama–Okado. Furthermore, we investigate an inhomogeneous generalization of the three-dimensional lattice model. We show that the inhomogeneous analog of (a certain subclass of) partition functions can be expressed as loop elementary symmetric functions.
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