Tetrahedron Equation and Quantum R Matrices for Spin Representations of B⁽¹⁾ₙ, D⁽¹⁾ₙ and D⁽²⁾ₙ₊₁

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It is known that a solution of the tetrahedron equation generates infinitely many solutions of the Yang-Baxter equation via suitable reductions. In this paper this scheme is applied to an oscillator solution of the tetrahedron equation involving bosons and fermions by using special 3d boundary conditions. The resulting solutions of the Yang-Baxter equation are identified with the quantum R matrices for the spin representations of B⁽¹⁾ₙ, D⁽¹⁾ₙ and D⁽²⁾ₙ₊₁.