Abstract:
This paper presents a construction of an infinite-dimensional solution of the Yang–Baxter equation of rank 1 which is represented as an integral operator with an elliptic hypergeometric kernel acting in the space of functions of two complex variables. This RR-operator intertwines the product of two standard LL-operators associated with the Sklyanin algebra, an elliptic deformation of the algebra sl(2)sl(2). The solution is constructed from three basic operators S1S1, S2S2, and S3S3 generating the permutation group S4 on four parameters. Validity of the key Coxeter relations (including a star-triangle relation) is based on the formula for computing an elliptic beta integral and the Bailey lemma associated with an elliptic Fourier transformation. The operators Sj are determined uniquely with the help of the elliptic modular double.
Bibliography: 37 titles.
Citation:
S. È. Derkachev, V. P. Spiridonov, “Yang–Baxter equation, parameter permutations, and the elliptic beta integral”, Russian Math. Surveys, 68:6 (2013), 1027–1072
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