Related papers: Super Solutions of the Dynamical Yang-Baxter Equat…
A generalization of the Yang-Baxter equation is proposed. It enables to construct integrable two-dimensional lattice models with commuting two-layer transfer matrices, while single-layer ones are not necessarily commutative. Explicit…
We introduce a class of new integrable lattice models labeled by a pair of positive integers N and r. The integrable model is obtained from the Gauge/YBE correspondence, which states the equivalence of the 4d N=1 S^1 \times S^3/Z_r index of…
We classify the finite-dimensional irreducible representations of the super Yangian associated with the orthosymplectic Lie superalgebra ${\frak osp}_{2|2n}$. The classification is given in terms of the highest weights and Drinfeld…
We obtain a new solution of the star-triangle relation with positive Boltzmann weights which contains as special cases all continuous and discrete spin solutions of this relation, that were previously known. This new master solution defines…
This paper gives some further details of proofs of some theorems related to the quantum dynamical Yang-Baxter equation. This mainly expands proofs given in "Lectures on the dynamical Yang-Baxter equation" by P. Etingof and O. Schiffmann,…
The type-I quantum superalgebras are known to admit non-trivial one-parameter families of inequivalent finite dimensional irreps, even for generic $q$. We apply the recently developed technique to construct new solutions to the quantum…
In 2001--2013 Derkachov and Manashov with coauthors obtained simple and natural expressions of $R$-matrices for the principal series of representations of the groups $\mathrm{SL}(2,\mathbb{C})$, $\mathrm{SL}(2,\mathbb{R})$,…
We show that Belavin's solutions of the quantum Yang--Baxter equation can be obtained by restricting an infinite $R$-matrix to suitable finite dimensional subspaces. This infinite $R$-matrix is a modified version of the Shibukawa--Ueno…
A new method for solving the Yang-Baxter equation is presented. It is based on the Taylor expansion of R-matrix which is developed up to the power lambda^6. Using this method the R-matrix for integrable spin ladder is calculated.
A dynamical $r$-matrix is associated with every self-dual Lie algebra $\A$ which is graded by finite-dimensional subspaces as $\A=\oplus_{n \in \cZ} \A_n$, where $\A_n$ is dual to $\A_{-n}$ with respect to the invariant scalar product on…
We will present solutions to the constant Yang-Baxter equation, in any dimension $n$. More precisely, for any $n$, we will create an infinite family of $n^2$ by $n^2$ matrices which are solutions to the constant Yang-Baxter equation. The…
We obtain inequivalent classical r-matrices of the $osp(1|2)$ Lie superalgebra as real solutions of the graded (modified) classical Yang-Baxter equation, in such a way that the corresponding automorphism transformation is employed. Then,…
We quantize the Alekseev-Meinrenken solution r to the classical dynamical Yang-Baxter equation, associated to a Lie algebra g with an element t in S^2(g)^g. Namely, we construct a dynamical twist J with nonabelian base in the sense of P.…
In this paper we introduce a procedure that, given a solution to the Yang-Baxter equation as input, produces a stochastic (or Markovian) solution to (a possibly dynamical version of) the Yang-Baxter equation. We then apply this…
The Yang-Baxter equation for a $SU(2)\times U(1)$-symmetric $S=1/2$ spin-orbital chain was solved using the special computer algorithm developed by the author. The 8 new $R$-matrices separated on 5 groups are presented. Among the obtained…
We have found some new solutions of both rational and trigonometric types by rewriting Yang-Baxter equation as a triple product equation in a vector space of matrices.
Involutive non-degenerate set theoretic solutions of the Yang-Baxter equation are considered, with a focus on finite solutions. A rich class of indecomposable and irretractable solutions is determined and necessary and sufficient conditions…
We construct sets of structure matrices for the semi-dynamical reflection algebra, solving the Yang-Baxter type consistency equations extended by the action of an automorphism of the auxiliary space. These solutions are parametrized by…
We study the existence problem for Novikov algebra structures on finite-dimensional Lie algebras. We show that a Lie algebra admitting a Novikov algebra is necessarily solvable. Conversely we present a $2$-step solvable Lie algebra without…
We study integrable dynamical systems described by a Lax pair involving a spectral parameter. By solving the classical Yang-Baxter equation when the R-matrix has two poles we show that they can be interpreted as natural motions on a twisted…