Related papers: Construction of $R$-matrices for symmetric tensor …
The integrable structure of the one-dimensional Hubbard model is based on Shastry's R-matrix and the Yangian of a centrally extended sl(2|2) superalgebra. Alcaraz and Bariev have shown that the model admits an integrable deformation whose…
We associate a deformation of Heisenberg algebra to the suitably normalized Yang $R$-matrix and we investigate its properties. Moreover, we construct new examples of quantum vertex algebras which possess the same representation theory as…
An elliptic deformation of $\widehat{sl}_2$ is proposed. Our presentation of the algebra is based on the relation $RLL=LLR^*$, where $R$ and $R^*$ are eight-vertex $R$-matrices with the elliptic moduli chosen differently. In the…
We consider the $R$-matrix presentations of the quantum queer superalgebra $U_q(q_n)$ and its affine counterpart $U_q(\widehat q_n)$. We derive crossing symmetry relations for the $R$-matrices and use them to construct central elements in…
We introduce an $R$-matrix acting on the tensor product of MacMahon representations of Ding-Iohara-Miki (DIM) algebra $U_{q,t}(\widehat{\widehat{\mathfrak{gl}}}_1)$. This $R$-matrix acts on pairs of $3d$ Young diagrams and retains the nice…
This text investigates relations between two well-known family of algorithms, matrix factorisations and recursive linear filters, by describing a probabilistic model in which approximate inference corresponds to a matrix factorisation…
The Universal T-matrix is the capstone of the structure that consists of a quantum group and its dual, and the central object from which spring the T-matrices (monodromies) of all the associated integrable models. A closed expression is…
The quantum Clebsch-Gordan coefficients and the explicit form of the $\breve{R}_{q}$ matrix related with the minimal representation of the quantum enveloping algebra $U_{q}E_{7}$ are calculated in this paper.
We find the complete set of invertible solutions of the untwisted and twisted reflection equations for the Bazhanov-Jimbo R-matrix of type ${\mathrm A}^{(1)}_{N-1}$. We also show that all invertible solutions can be obtained by an…
We study the highest weight representations of the RTT algebras for the R matrix of sp_q(2n) type by the nested algebraic Bethe ansatz. It is a generalization of our study for R matrix of sp(2n) and so(2n) type
We recall the classification of the irreducible representations of $SL(2)_q$, and then give fusion rules for these representations. We also consider the problem of $\cR$-matrices, intertwiners of the differently ordered tensor products of…
We consider $\rm R$-matrix realization of the quantum deformations of the loop algebras $\tilde{\mathfrak{g}}$ corresponding to non-exceptional affine Lie algebras of type $\hat{\mathfrak{g}}=A^{(1)}_{N-1}$, $B^{(1)}_n$, $C^{(1)}_n$,…
We introduce the two-parameter quantum affine algebra $U_{r,s}(\widehat{gl}_n)$ via the RTT realization. The Drinfeld realization is given and the type A quantum affine algebra is proved to be a special subalgebra of our extended algebra.
In this paper we will give a similar factorization as in \cite{4}, \cite{5}, where the autors Svrtan and Meljanac examined certain matrix factorizations on Fock-like representation of a multiparametric quon algebra on the free associative…
In this paper we investigate the algebraic structure of AdS/CFT in the strong-coupling limit. We propose an expression for the classical r-matrix with (deformed) u(2|2) symmetry, which leads to a quasi-triangular Lie bialgebra as the…
The intertwiner of the quantized coordinate ring $A_q(sl_3)$ is known to yield a solution to the tetrahedron equation. By evaluating their $n$-fold composition with special boundary vectors we generate series of solutions to the Yang-Baxter…
We analyze effective approximation of unitary matrices. In our formulation, a unitary matrix is represented as a product of rotations in two-dimensional subspaces, so-called Givens rotations. Instead of the quadratic dimension dependence…
We construct the Drinfeld twists (or factorizing $F$-matrices) of the supersymmetric model associated with quantum superalgebra $U_q(gl(m|n))$, and obtain the completely symmetric representations of the creation operators of the model in…
We show that the truncation of twisted Yangians are isomorphic to finite W-algebras based on orthogonal or symplectic algebras. This isomorphism allows us to classify all the finite dimensional irreducible representations of the quoted…
At leading order, the $S$-matrices in QED and gravity are known to factorise, providing unambiguous determinations of the parts divergent due to infrared contributions. The soft $S$-matrices defined in this fashion are shown to be defined…