arXiv subjects
Publications and source records attributed to M. Samsonov.
We give a rigorous treatment to the thermodynamic limit of the 6-vertex model. We prove that the unique solution of the Bethe-Ansatz equation exists and the distribution of the roots converges to a continuum measure. We solve this problem for $0<Δ<1$ using convexity arguments and for large negative $Δ$ using the Fixed Point Theory of appropriately defined contracting operator.
We propose a method of quantization of certain Lie bialgebra structures on the polynomial Lie algebras related to quasi-trigonometric solutions of the classical Yang-Baxter equation. The method is based on so-called affinization of certain seaweed algebras and their quantum analogues.
We propose a method of quantization of certain Lie bialgebra structures on the polynomial Lie algebras related to quasi-trigonometric solutions of the classical Yang--Baxter equation. The method is based on an affine realization of certain seaweed algebras and their quantum analogues. We also propose a method of $ω$-affinization, which enables us to quantize rational $r$-matrices of $\mathfrak{sl}(3)$.
We obtain explicit formulas for the semi-classical twists deforming the coalgebraic structure of U(sl(3)) and U(sl(4)). In rank 2 and 3 the corresponding universal R-matrices quantize the boundary r-matrices of Cremmer-Gervais type defining Lie Frobenius structures on the maximal parabolic subalgebras in sl(n).