As a mathematician working the area of representation of Quantum groups, I am constantly thinking about solutions of the Yang-Baxter equation. In particular, trigonometric solutions.

Often research grants in this area cite this as an "application" of their research. This being said, many mathematicians(definitely including myself) don't know why these solutions are important. So, I wonder;

What exactly do physicists do with solutions to the Yang-Baxter Equation once they have them?

Thanks.

As a mathematician working the area of representation of Quantum groups, I am constantly thinking about solutions of the Yang-Baxter equation. In particular, trigonometric solutions.

Often research grants in this area cite this as an "application" of their research. This being said, many mathematicians  (definitely including myself) don't know why these solutions are important. So, I wonder:

What exactly do physicists do with solutions to the Yang-Baxter Equation once they have them?