Kirillov, Grothendieck polynomials and the Yang-Baxter equation, in Formal power series and algebraic combinatorics/Series formelles et combinatoire algebrique (University of Rutgers, Piscataway, 1994), 183-189, DIMACS, Piscataway, NJ, s.
In  and , Fomin and Kirillov introduced [beta]-Grothendieck polynomials in the framework of Yang-Baxter equations together with their combinatorial formula and showed that they coincide with the ones defined by Lascoux and Schutzenberger with the specialization [beta] = - 1.
She covers seaweed meanders, meanders, Morse meanders and Sturm global attractors, right and left one-shifts, connection graphs of types I through IV, meanders and the Temperley-Lieb algebra, representations of seaweed Lie algebras, and classical Yang-Baxter equation
Vector bundles on degenerations of elliptic curves and Yang-Baxter equations
On rational solutions of Yang-Baxter equation for sl(n).
Constant solutions of Yang-Baxter equation for sl(2) and sl(3).
The following lemma gives a (now classical) example of use of the Yang-Baxter equation.
We will need the following application of the Yang-Baxter equation, which allows, under certain condition, a line with a change of parameter to go through a grid.
Key words: Lie bialgebras, Hopf algebras, Poisson brackets, Lie Poisson group, Hopf co-Poisson algebra, Universal enveloping algebra, r-matrix, Quantum group, Yang-Baxter equation.
To achieve this purpose we use a solution of the classical Yang-Baxter equation (CYBE) on Lie algebra ST(2).
There are techniques for solving the Yang-Baxter equation
In this graduate-level text the authors introduce the Yang-Baxter equation
and its applications, an important are in representation theory and quantum groups.