131 citations · 1.2k across the 53 of their papers we have counts for
15 papers · 1 filter
Graphical calculus for quantum vertex operators, I: The dynamical fusion operator
Hadewijch De Clercq, Nicolai Reshetikhin, Jasper Stokman
This paper is the first in a series on graphical calculus for quantum vertex operators. We establish in great detail the foundations of graphical calculus for ribbon categories and…
Integral solutions to boundary quantum Knizhnik-Zamolodchikov equations
Nicolai Reshetikhin, Jasper Stokman, Bart Vlaar
We construct integral representations of solutions to the boundary quantum Knizhnik-Zamolodchikov equations. These are difference equations taking values in tensor products of Verm…
Boundary quantum Knizhnik-Zamolodchikov equations and fusion
Nicolai Reshetikhin, Jasper Stokman, Bart Vlaar
In this paper we extend our previous results concerning Jackson integral solutions of the boundary quantum Knizhnik-Zamolodchikov equations with diagonal K-operators to higher-spin…
Recursion Formulas for HOMFLY and Kauffman Invariants
Qingtao Chen, Nicolai Reshetikhin
In this note we describe the recursion relations between two parameter HOMLFY and Kauffman polynomials of framed links These relation correspond to embeddings of quantized universa…
Boundary quantum Knizhnik-Zamolodchikov equations and Bethe vectors
Nicolai Reshetikhin, Jasper Stokman, Bart Vlaar
Solutions to boundary quantum Knizhnik-Zamolodchikov equations are constructed as bilateral sums involving "off-shell" Bethe vectors in case the reflection matrix is diagonal and o…
Geometry of the analytic loop group
Corrado De Concini, David Hernandez, Nicolai Reshetikhin
We introduce and study a notion of analytic loop group with a Riemann-Hilbert factorization relevant for the representation theory of quantum affine algebras at roots of unity with…
Poisson Lie groups and Hamiltonian theory of the Yang-Baxter maps
Nicolai Reshetikhin, Alexander Veselov
We show how the theory of Poisson Lie groups can be used to establish the Poisson properties of the Yang-Baxter maps and related transfer dynamics. As an example we present the Ham…
Braiding for the quantum gl_2 at roots of unity
R. Kashaev, N. Reshetikhin
In our preceding papers we started considering the categories of tangles with flat G-connections in their complements, where G is a simple complex algebraic group. The braiding (or…
Hopf algebras with trace and representations
C. DeConcini, C. Procesi, N. Reshetikhin +1
We study the restriction of representations of Cayley-Hamilton algebras to subalgebras. This theory is applied to determine tensor products and branching rules for representations…
Symmetrically Factorizable Groups and Set-Theoretical Solutions of the Pentagon Equation
R. M. Kashaev, N. Reshetikhin
The notion of a symmetrically factorizable Lie group is introduced. It is shown that each symmetrically factorizable Lie group is related to a set-theoretical solution of the penta…
Integrability of characteristic Hamiltonian systems on simple Lie groups with standard Poisson Lie structure
Nicolai Reshetikhin
Phase space of a characteristic Hamiltonian system is a symplectic leaf of a factorizable Poisson Lie group. Its Hamiltonian is a restriction to the symplectic leaf of a function o…
Quantum invariant measures
Nicolai Reshetikhin, Milen Yakimov
We derive an explicit expression for the Haar integral on the quantized algebra of regular functions C_q[K] on the compact real form K of an arbitrary simply connected complex simp…
Deformation Quantization of Kahler Manifolds
Nicolai Reshetikhin, Leon Takhtajan
We present an explicit formula for the deformation quantization on Kähler manifolds.
Deformation Quantization of Lagrangian Fiber Bundles
Nicolai Reshetikhin, Milen Yakimov
Let (M, \om) be a symplectic manifold. A Lagrangian fiber bundle π: M -> B determines a completely integrable system on M. First integrals of this system are the pull-backs of func…
The q-characters of representations of quantum affine algebras and deformations of W-algebras
Edward Frenkel, Nicolai Reshetikhin
We propose the notion of q-characters for finite-dimensional representations of quantum affine algebras. It is motivated by our theory of deformed W-algebras. We show that the q-ch…