### 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

Kojima, T., Konno, H., & Weston, R. (2005). The vertex-face correspondence and correlation functions of the fusion eight-vertex model. I: The general formalism.

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