On the degenerate multiplicity of the loop algebra for the 6V transfer matrix at roots of unity.
On the exponential representation of .
On the problem of classifying simple compact quantum groups
We review the notion of simple compact quantum groups and examples, and discuss the problem of construction and classification of simple compact quantum groups.
On the q-exponential of matrix q-Lie algebras
In this paper, we define several new concepts in the borderline between linear algebra, Lie groups and q-calculus.We first introduce the ring epimorphism r, the set of all inversions of the basis q, and then the important q-determinant and corresponding q-scalar products from an earlier paper. Then we discuss matrix q-Lie algebras with a modified q-addition, and compute the matrix q-exponential to form the corresponding n × n matrix, a so-called q-Lie group, or manifold, usually with q-determinant...
On the set-theoretical Yang-Baxter equation.
On two possible constructions of the quantum semigroup of all quantum permutations of an infinite countable set
Two different models for a Hopf-von Neumann algebra of bounded functions on the quantum semigroup of all (quantum) permutations of infinitely many elements are proposed, one based on projective limits of enveloping von Neumann algebras related to finite quantum permutation groups, and the second on a universal property with respect to infinite magic unitaries.
One-dimensional vertex models associated with a class of Yangian invariant Haldane-Shastry like spin chains.
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 .
-analog of Gelfand-Graev basis for the noncompact quantum algebra .
-boson in quantum integrable systems.
-deformation of the Virasoro algebra and lattice conformal theories
-deformed bi-local fields. II.