Parameter-dependent solutions of the classical Yang-Baxter equation on .
Paths and tableaux descriptions of Jacobi-Trudi determinant associated with quantum affine algebra of type .
PBW and duality theorems for quantum groups and quantum current algebras.
PBW-bases of quantum groups.
Poisson Lie groups and their relations to quantum groups
The notion of Poisson Lie group (sometimes called Poisson Drinfel'd group) was first introduced by Drinfel'd [1] and studied by Semenov-Tian-Shansky [7] to understand the Hamiltonian structure of the group of dressing transformations of a completely integrable system. The Poisson Lie groups play an important role in the mathematical theories of quantization and in nonlinear integrable equations. The aim of our lecture is to point out the naturality of this notion and to present basic facts about...
Positivity of the -system cluster algebra.
Primitive Ideals and Symplectic Leaves of Quantum Matrices
It is proved that there exists a bijection between the primitive ideals of the algebra of regular functions on quantum m × n-matrices and the symplectic leaves of associated Poisson structure.
Problems in the theory of quantum groups
This is a collection of open problems in the theory of quantum groups. Emphasis is given to problems in the analytic aspects of the subject.
Promotion operator on rigged configurations of type .