# SHIBUKAWA, Youichi:Department of Mathematics,Faculty of Science,Associate Professor,Algebra

- Keyword(s):
- (Dynamical) Yang-Baxter equation, Representation theory of quantum groups, (Elliptic) R-operator
- Research Interest:
- Infinite analysis; Integrable systems
- Research Activities:
- My research area is: (1) dynamical Yang-Baxter maps; (2) (elliptic, trigonometric, and rational) R-operators; (3) representation theory of quantum groups.
The dynamical Yang-Baxter map is a set-theoretical solution to a version of the quantum dynamical Yang-Baxter equation. This concept is a generalization of the Yang-Baxter map, a set-theoretical solution to the quantum Yang-Baxter equation.
The R-operator is a solution to the quantum Yang-Baxter equation on a function space. Most generalized one is called the elliptic R-operator, because it is expressed by means of the elliptic theta function. This elliptic R-operator is a generalization of Belevin's Z_n symmetric R-matrix.