### Abstract

By making use of the vertex-face correspondence, we give an algebraic analysis formulation of correlation functions of the k × k fusion eight-vertex model in terms of the corresponding fusion SOS model. Here k ? Z_{>0}. A general formula for correlation functions is derived as a trace over the space of states of lattice operators such as the corner-transfer matrices, the half-transfer matrices (vertex operators) and the tail operator. We give a realization of these lattice operators as well as the space of states as objects in the level k representation theory of the elliptic algebra U_{q,p} (sl_{2}). © 2005 Elsevier B.V. All rights reserved.

Original language | English |
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Pages (from-to) | 348-398 |

Number of pages | 51 |

Journal | Nuclear Physics B |

Volume | 720 |

Issue number | 3 |

DOIs | |

Publication status | Published - 8 Aug 2005 |

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### Cite this

*Nuclear Physics B*,

*720*(3), 348-398. https://doi.org/10.1016/j.nuclphysb.2005.05.012

}

*Nuclear Physics B*, vol. 720, no. 3, pp. 348-398. https://doi.org/10.1016/j.nuclphysb.2005.05.012

**The vertex-face correspondence and correlation functions of the fusion eight-vertex model. I : The general formalism.** / Kojima, Takeo; Konno, Hitoshi; Weston, Robert.

Research output: Contribution to journal › Article

TY - JOUR

T1 - The vertex-face correspondence and correlation functions of the fusion eight-vertex model. I

T2 - The general formalism

AU - Kojima, Takeo

AU - Konno, Hitoshi

AU - Weston, Robert

PY - 2005/8/8

Y1 - 2005/8/8

N2 - By making use of the vertex-face correspondence, we give an algebraic analysis formulation of correlation functions of the k × k fusion eight-vertex model in terms of the corresponding fusion SOS model. Here k ? Z>0. A general formula for correlation functions is derived as a trace over the space of states of lattice operators such as the corner-transfer matrices, the half-transfer matrices (vertex operators) and the tail operator. We give a realization of these lattice operators as well as the space of states as objects in the level k representation theory of the elliptic algebra Uq,p (sl2). © 2005 Elsevier B.V. All rights reserved.

AB - By making use of the vertex-face correspondence, we give an algebraic analysis formulation of correlation functions of the k × k fusion eight-vertex model in terms of the corresponding fusion SOS model. Here k ? Z>0. A general formula for correlation functions is derived as a trace over the space of states of lattice operators such as the corner-transfer matrices, the half-transfer matrices (vertex operators) and the tail operator. We give a realization of these lattice operators as well as the space of states as objects in the level k representation theory of the elliptic algebra Uq,p (sl2). © 2005 Elsevier B.V. All rights reserved.

UR - http://www.scopus.com/inward/record.url?scp=21744454532&partnerID=8YFLogxK

U2 - 10.1016/j.nuclphysb.2005.05.012

DO - 10.1016/j.nuclphysb.2005.05.012

M3 - Article

VL - 720

SP - 348

EP - 398

JO - Nuclear Physics B

JF - Nuclear Physics B

SN - 0550-3213

IS - 3

ER -