Thursday, May 17, 2012

1205.3520 (S. E. Derkachov et al.)

Yang-Baxter equation, parameter permutations, and the elliptic beta

S. E. Derkachov, V. P. Spiridonov
We construct the general solution of the Yang-Baxter equation which is represented as an integral operator with an elliptic hypergeometric kernel acting in the space of functions of two complex variables. It intertwines the product of two standard L-operators associated with the Sklyanin algebra, an elliptic deformation of sl(2). This R-operator is constructed from three basic operators $S_1, S_2$ and $S_3$ generating the permutation group of four parameters $\mathfrak{S}_4$. Validity of the key Coxeter relations is based on the elliptic beta integral evaluation formula and the Bailey lemma associated with an elliptic Fourier transformation. The operators $S_j$ are determined uniquely with the help of an elliptic modular double.
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