A particular solution of a Painlevé system in terms of the hypergeometric function .
Almost-graded central extensions of Lax operator algebras
Lax operator algebras constitute a new class of infinite dimensional Lie algebras of geometric origin. More precisely, they are algebras of matrices whose entries are meromorphic functions on a compact Riemann surface. They generalize classical current algebras and current algebras of Krichever-Novikov type. Lax operators for 𝔤𝔩(n), with the spectral parameter on a Riemann surface, were introduced by Krichever. In joint works of Krichever and Sheinman their algebraic structure was revealed and...
Classical -operators and integrable generalizations of Thirring equations.
Clifford algebra derivations of tau-functions for two-dimensional integrable models with positive and negative flows.
Completely Integrable Hamiltonian Systems Connected with Semisimple Lie Algebras.
Coordinate Bethe ansatz for spin XXX model.
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...
Ermakov's superintegrable toy and nonlocal symmetries.
Hidden symmetries of stochastic models.
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.
Intertwining symmetry algebras of quantum superintegrable systems.
Junction type representations of the Temperley-Lieb algebra and associated symmetries.
Limits of Gaudin systems: classical and quantum cases.
Models of quadratic algebras generated by superintegrable systems in 2D.
-wave equations with orthogonal algebras: and reductions and soliton solutions.
On a family of operators and their Lie algebras.
Para-Grassmann variables and coherent states.
Positivity of the -system cluster algebra.
Quadratic homogeneous ODE systems of Jordan-rigid body type.
Quantum deformations and superintegrable motions on spaces with variable curvature.