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Free field constructions for the elliptic algebra ${\cal A}_{q,p}(\hat{sl}_2)$ and Baxter's eight-vertex model

Jun'ichi Shiraishi
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Abstract

Three examples of free field constructions for the vertex operators of the elliptic quantum group ${\cal A}_{q,p}(\hat{sl}_2)$ are obtained. Two of these (for $p^{1/2}=\pm q^{3/2},p^{1/2}=-q^2$) are based on representation theories of the deformed Virasoro algebra, which correspond to the level 4 and level 2 $Z$-algebra of Lepowsky and Wilson. The third one ($p^{1/2}=q^{3}$) is constructed over a tensor product of a bosonic and a fermionic Fock spaces. The algebraic structure at $p^{1/2}=q^{3}$, however, is not related to the deformed Virasoro algebra. Using these free field constructions, an integral formula for the correlation functions of Baxter's eight-vertex model is obtained. This formula shows different structure compared with the one obtained by Lashkevich and Pugai.

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Jun'ichi Shiraishi. 2003-04-21. Free field constructions for the elliptic algebra ${\cal A}_{q,p}(\hat{sl}_2)$ and Baxter's eight-vertex model. https://doi.org/10.1142/s0217751x0402052x

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