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

Atsuo Kuniba, Sergey Sergeev

    Research output: Contribution to journalArticle

    10 Citations (Scopus)

    Abstract

    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)nBn(1), D(1)nDn(1) and D(2)n+1Dn+1(2).
    Original languageEnglish
    Pages (from-to)695-713
    Number of pages19
    JournalCommunications in Mathematical Physics
    Volume324
    Issue number3
    DOIs
    Publication statusPublished - 2013

    Fingerprint

    Yang-Baxter Equation
    Triangular pyramid
    R-matrix
    tetrahedrons
    Infinitely Many Solutions
    Bosons
    Fermions
    Boundary conditions
    bosons
    fermions
    oscillators
    boundary conditions

    Cite this

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    abstract = "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)nBn(1), D(1)nDn(1) and D(2)n+1Dn+1(2).",
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    Tetrahedron Equation and Quantum R Matrices for Spin Representations of B(1) nD(1) n and D(2) n+1. / Kuniba, Atsuo; Sergeev, Sergey.

    In: Communications in Mathematical Physics, Vol. 324, No. 3, 2013, p. 695-713.

    Research output: Contribution to journalArticle

    TY - JOUR

    T1 - Tetrahedron Equation and Quantum R Matrices for Spin Representations of B(1) nD(1) n and D(2) n+1

    AU - Kuniba, Atsuo

    AU - Sergeev, Sergey

    PY - 2013

    Y1 - 2013

    N2 - 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)nBn(1), D(1)nDn(1) and D(2)n+1Dn+1(2).

    AB - 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)nBn(1), D(1)nDn(1) and D(2)n+1Dn+1(2).

    KW - (blank)

    U2 - 10.1007/s00220-013-1808-9

    DO - 10.1007/s00220-013-1808-9

    M3 - Article

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    SP - 695

    EP - 713

    JO - Communications in Mathematical Physics

    JF - Communications in Mathematical Physics

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