### Abstract

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.

Original language | English |
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Pages (from-to) | 447-461 |

Number of pages | 15 |

Journal | Letters in Mathematical Physics |

Volume | 105 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2015 |

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## Cite this

Kuniba, A., Okado, M., & Sergeev, S. (2015). Tetrahedron Equation and Quantum R Matrices for Modular Double of Uq(D(2) n+1), Uq(A(2) 2n) and Uq(C(1) n).

*Letters in Mathematical Physics*,*105*(3), 447-461. https://doi.org/10.1007/s11005-015-0747-0