Mathematics – Quantum Algebra
Scientific paper
2003-02-10
Int.J.Mod.Phys. A19S2 (2004) 363-380
Mathematics
Quantum Algebra
23 pages. Based on talks given at "MATHPHYS ODYSSEY 2001-Integrable Models and Beyond" at Okayama and Kyoto, February 19-23, 2
Scientific paper
10.1142/S0217751X0402052X
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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