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

Atsuo Kuniba, M Okado, Sergey Sergeev

    Research output: Contribution to journalArticle

    4 Citations (Scopus)

    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 languageEnglish
    Pages (from-to)447-461
    Number of pages15
    JournalLetters in Mathematical Physics
    Volume105
    Issue number3
    DOIs
    Publication statusPublished - 2015

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    Quantum Affine Algebra
    Triangular pyramid
    R-matrix
    tetrahedrons
    algebra
    Yang-Baxter Equation
    Commutativity
    Commute
    Homomorphism
    Tensor Product
    Fold
    Algebra
    oscillators
    tensors
    products

    Cite this

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    title = "Tetrahedron Equation and Quantum R Matrices for Modular Double of Uq(D(2) n+1), Uq(A(2) 2n) and Uq(C(1) n)",
    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.",
    keywords = "Tetrahedron equation, q-oscillator algebra, Yang-Baxter equation, modular double",
    author = "Atsuo Kuniba and M Okado and Sergey Sergeev",
    year = "2015",
    doi = "10.1007/s11005-015-0747-0",
    language = "English",
    volume = "105",
    pages = "447--461",
    journal = "Letters in Mathematical Physics",
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    }

    Tetrahedron Equation and Quantum R Matrices for Modular Double of Uq(D(2) n+1), Uq(A(2) 2n) and Uq(C(1) n). / Kuniba, Atsuo; Okado, M; Sergeev, Sergey.

    In: Letters in Mathematical Physics, Vol. 105, No. 3, 2015, p. 447-461.

    Research output: Contribution to journalArticle

    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 -