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The Vertex-Face Correspondence and Correlation Functions of the Fusion Eight-Vertex Model I: The General Formalism

Takeo Kojima·Hitoshi Konno·Robert Weston
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Abstract

Based on the vertex-face correspondence, we give an algebraic analysis formulation of correlation functions of the $k\times k$ fusion eight-vertex model in terms of the corresponding fusion SOS model. Here $k\in Z_{>0}$. 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 $U_{q,p}(\hat{sl}_2)$.

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BibTeXRIS

Takeo Kojima, Hitoshi Konno, Robert Weston. 2005-05-17. The Vertex-Face Correspondence and Correlation Functions of the Fusion Eight-Vertex Model I: The General Formalism. https://doi.org/10.1016/j.nuclphysb.2005.05.012

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