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A class of partition functions associated with \(E_{\tau,\eta}gl_3\) by Izergin-Korepin analysis. (English) Zbl 1443.81041

Summary: Recently, a class of partition functions associated with higher rank rational and trigonometric integrable models were introduced by Foda and Manabe. We use the dynamical \(R\)-matrix of the elliptic quantum group \(E_{\tau,\eta}(gl_3)\) to introduce an elliptic analog of the partition functions associated with \(E_{\tau,\eta}(gl_3)\). We investigate the partition functions of Foda-Manabe type by developing a nested version of the elliptic Izergin-Korepin analysis and present the explicit forms as symmetrization of multivariable elliptic functions. We show that special cases are essentially the elliptic weight functions introduced in the works by Rimányi, Tarasov, and Varchenko; Konno; and Felder, Rimányi, and Varchenko.
©2020 American Institute of Physics

MSC:

81R12 Groups and algebras in quantum theory and relations with integrable systems
81R50 Quantum groups and related algebraic methods applied to problems in quantum theory
17B37 Quantum groups (quantized enveloping algebras) and related deformations
33E05 Elliptic functions and integrals
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