Tetrahedron Equation and Quantum R Matrices for q-Oscillator Representations Mixing Particles and Holes

Abstract

We construct 2ⁿ+1 solutions to the Yang-Baxter equation associated with the quantum affine algebras Uq(A⁽¹⁾ₙ₋₁), Uq(A⁽²⁾₂ₙ), Uq(C⁽¹⁾ₙ), and Uq(D⁽²⁾ₙ₊₁). They act on the Fock spaces of an arbitrary mixture of particles and holes in general. Our method is based on new reductions of the tetrahedron equation and an embedding of the quantum affine algebras into n copies of the q-oscillator algebra, which admits an automorphism interchanging particles and holes.