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Yang-Baxter equation, elliptic hypergeometric integrals, and ABS equations.

Hold Date
2017-07-20 16:30〜2017-07-20 17:30
Lecture Room S W1-C-503, West Zone 1, Ito campus, Kyushu University
Object person
Andrew Kels (University of Tokyo)

The Yang-Baxter equation is a key equation for integrability of two-dimensional models of statistical mechanics.  Particularly, for some lattice models, the Yang-Baxter equation takes a special form known as the "star-triangle relation".  The most general known forms of the Yang-Baxter equation for lattice models were recently found, that are expressed in terms of the elliptic gamma function, and are equivalent to transformation formulas of elliptic hypergeometric integrals.  This discovery has lead to new elliptic hypergeometric "sum/integral" transformation formulas, which involve a mixture of complex and integer valued variables, and contain the well known (e.g. A_n, BC_n) integral transformation formulas as special cases.  Furthermore, the quasi-classical asymptotics of the aforementioned Yang-Baxter equations, are directly associated to discrete integrable equations in the classification of Adler, Bobenko, and Suris (ABS).  This talk will give an overview of these results, based on some of the recent works of the speaker.