Seminar
YangBaxter equation, elliptic hypergeometric integrals, and ABS equations.

Hold Date 
20170720 16:30～20170720 17:30 


Place 
Lecture Room S W1C503, West Zone 1, Ito campus, Kyushu University 


Object person 



Speaker 
Andrew Kels (University of Tokyo) 

Abstract:
The YangBaxter equation is a key equation for integrability of twodimensional models of statistical mechanics. Particularly, for some lattice models, the YangBaxter equation takes a special form known as the "startriangle relation". The most general known forms of the YangBaxter 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 quasiclassical asymptotics of the aforementioned YangBaxter 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.