TY - JOUR

T1 - Tetrahedron Equation and Quantum R Matrices for Modular Double of Uq(D(2) n+1), Uq(A(2) 2n) and Uq(C(1) n)

AU - Kuniba, Atsuo

AU - Okado, M

AU - Sergeev, Sergey

PY - 2015

Y1 - 2015

N2 - We introduce a homomorphism from the quantum affine algebras Uq(D(2) n+1), Uq(A(2) 2n), Uq(C(1) n) to the n-fold tensor product of the q-oscillator algebra Aq. Their action commutes with the solutions of the Yang–Baxter equation obtained by reducing the solutions of the tetrahedron equation associated with the modular and the Fock representations of Aq. In the former case, the commutativity is enhanced to the modular double of these quantum affine algebras.

AB - We introduce a homomorphism from the quantum affine algebras Uq(D(2) n+1), Uq(A(2) 2n), Uq(C(1) n) to the n-fold tensor product of the q-oscillator algebra Aq. Their action commutes with the solutions of the Yang–Baxter equation obtained by reducing the solutions of the tetrahedron equation associated with the modular and the Fock representations of Aq. In the former case, the commutativity is enhanced to the modular double of these quantum affine algebras.

KW - Tetrahedron equation

KW - q-oscillator algebra

KW - Yang-Baxter equation

KW - modular double

U2 - 10.1007/s11005-015-0747-0

DO - 10.1007/s11005-015-0747-0

M3 - Article

VL - 105

SP - 447

EP - 461

JO - Letters in Mathematical Physics

JF - Letters in Mathematical Physics

SN - 0377-9017

IS - 3

ER -