Eigenvectors of open Bazhanov-Stroganov quantum chain.
Entwining Yang-Baxter maps and integrable lattices
Yang-Baxter (YB) map systems (or set-theoretic analogs of entwining YB structures) are presented. They admit zero curvature representations with spectral parameter depended Lax triples L₁, L₂, L₃ derived from symplectic leaves of 2 × 2 binomial matrices equipped with the Sklyanin bracket. A unique factorization condition of the Lax triple implies a 3-dimensional compatibility property of these maps. In case L₁ = L₂ = L₃ this property yields the set-theoretic quantum Yang-Baxter equation, i.e. the...
Finite-temperature form factors: a review.
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...
Generalized coherent states for -oscillator associated with discrete -Hermite polynomials.
Generalized Heisenberg algebras, SUSYQM and degeneracies: infinite well and Morse potential.
Generating series for nested Bethe vectors.
Integrability and diffeomorphisms on target space.
Integrable models of interaction of matter with radiation.
Integrable string models in terms of chiral invariants of groups.
Jacobi operators of quantum counterparts of three-dimensional real Lie algebras over the harmonic oscillator
Operadic Lax representations for the harmonic oscillator are used to construct the quantum counterparts of three-dimensional real Lie algebras. The Jacobi operators of these quantum algebras are explicitly calculated.
Junction type representations of the Temperley-Lieb algebra and associated symmetries.
Kernel functions for difference operators of Ruijsenaars type and their applications.
Limits of Gaudin systems: classical and quantum cases.
Littlewood-Richardson coefficients and integrable tilings.
Miura opers and critical points of master functions
Critical points of a master function associated to a simple Lie algebra come in families called the populations [11]. We prove that a population is isomorphic to the flag variety of the Langlands dual Lie algebra . The proof is based on the correspondence between critical points and differential operators called the Miura opers. For a Miura oper D, associated with a critical point of a population, we show that all solutions of the differential equation DY=0 can be written explicitly in terms...
Models for quadratic algebras associated with second order superintegrable systems in 2D.
Monopoles and modifications of bundles over elliptic curves.
On the degenerate multiplicity of the loop algebra for the 6V transfer matrix at roots of unity.
One-dimensional vertex models associated with a class of Yangian invariant Haldane-Shastry like spin chains.