### Abstract

The modified tetrahedron equation (MTE) with affine Weyl quantum variables at the Mb. root of unity is solved by a rational mapping operator which is obtained from the solution of a linear problem. We show that the solutions can be parametrized in terms of eight free parameters and 16 discrete phase choices, thus providing a broad starting point for the construction of three-dimensional integrable lattice models. The Fermat-curve points parametrizing the representation of the mapping operator in terms of cyclic functions are expressed in terms of the independent parameters. An explicit formula for the density factor of the MTE is derived. For the example N = 2 we write the MTE in full detail.

Original language | English |
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Pages (from-to) | 975-998 |

Number of pages | 24 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 36 |

Issue number | 4 |

DOIs | |

Publication status | Published - 31 Jan 2003 |

Externally published | Yes |

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*Journal of Physics A: Mathematical and General*,

*36*(4), 975-998. https://doi.org/10.1088/0305-4470/36/4/309

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*Journal of Physics A: Mathematical and General*, vol. 36, no. 4, pp. 975-998. https://doi.org/10.1088/0305-4470/36/4/309

**Explicit free parametrization of the modified tetrahedron equation.** / Von Gehlen, Gunter; Pakuliak, Stanislav; Sergeev, S.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Explicit free parametrization of the modified tetrahedron equation

AU - Von Gehlen, Gunter

AU - Pakuliak, Stanislav

AU - Sergeev, S.

PY - 2003/1/31

Y1 - 2003/1/31

N2 - The modified tetrahedron equation (MTE) with affine Weyl quantum variables at the Mb. root of unity is solved by a rational mapping operator which is obtained from the solution of a linear problem. We show that the solutions can be parametrized in terms of eight free parameters and 16 discrete phase choices, thus providing a broad starting point for the construction of three-dimensional integrable lattice models. The Fermat-curve points parametrizing the representation of the mapping operator in terms of cyclic functions are expressed in terms of the independent parameters. An explicit formula for the density factor of the MTE is derived. For the example N = 2 we write the MTE in full detail.

AB - The modified tetrahedron equation (MTE) with affine Weyl quantum variables at the Mb. root of unity is solved by a rational mapping operator which is obtained from the solution of a linear problem. We show that the solutions can be parametrized in terms of eight free parameters and 16 discrete phase choices, thus providing a broad starting point for the construction of three-dimensional integrable lattice models. The Fermat-curve points parametrizing the representation of the mapping operator in terms of cyclic functions are expressed in terms of the independent parameters. An explicit formula for the density factor of the MTE is derived. For the example N = 2 we write the MTE in full detail.

KW - modified tetrahedron equation

UR - http://www.scopus.com/inward/record.url?scp=0037474397&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/36/4/309

DO - 10.1088/0305-4470/36/4/309

M3 - Article

VL - 36

SP - 975

EP - 998

JO - Journal of Physics A: Mathematical and General

JF - Journal of Physics A: Mathematical and General

SN - 1751-8113

IS - 4

ER -