-matrix and Baxter -operators for the noncompact invariant spin chain.
A critical phenomenon in solitonic Ising chains.
Algebro-geometric Approach to the Yang-Baxter Equation and Related Topics
An analytic formula for the Jack polynomials.
Asymptotics for random walks in alcoves of affine Weyl groups.
Bethe Ansatz and the geography of rigged strings
We demonstrate the way in which composition of two famous combinatorial bijections, of Robinson-Schensted and Kerov-Kirillov-Reshetikhin, applied to the Heisenberg model of magnetic ring with spin 1/2, defines the geography of rigged strings (which label exact eigenfunctions of the Bethe Ansatz) on the classical configuration space (the set of all positions of the system of r reversed spins). We point out that each l-string originates, in the language of this bijection, from an island of l consecutive...
Bethe ansatz, inverse scattering transform and tropical Riemann theta function in a periodic soliton cellular automaton for .
Bethe ansatz solutions to quasi exactly solvable difference equations.
Combinatorics of the three-parameter PASEP partition function.
Construction of the Bethe state for the elliptic quantum group.
Coordinate Bethe ansatz for spin XXX model.
Correlation function and simplified TBA equations for XXZ chain.
Dynamical matrices of elliptic quantum groups and connection matrices for the -KZ equations.
Eigenvectors of open Bazhanov-Stroganov quantum chain.
Fermionic basis in conformal field theory and thermodynamic Bethe ansatz for excited states.
Gaudin's model and the generating function of the Wroński map
We consider the Gaudin model associated to a point z ∈ ℂⁿ with pairwise distinct coordinates and to the subspace of singular vectors of a given weight in the tensor product of irreducible finite-dimensional sl₂-representations, [G]. The Bethe equations of this model provide the critical point system of a remarkable rational symmetric function. Any critical orbit determines a common eigenvector of the Gaudin hamiltonians called a Bethe vector. In [ReV], it was shown that for generic...
Generating operator of or Gaudin transfer matrices has quasi-exponential kernel.
Gibbsian fields associated to exponentially decreasing quadratic potentials
Higher SPIN alternating sign matrices.
Hypergeometric solutions of the quantum differential equation of the cotangent bundle of a partial flag variety
We describe hypergeometric solutions of the quantum differential equation of the cotangent bundle of a partial flag variety. These hypergeometric solutions manifest the Landau-Ginzburg mirror symmetry for the cotangent bundle of a partial flag variety.