Related papers: Construction of $R$-matrices for symmetric tensor …
A description of the embedding of the universal Askey--Wilson algebra, AW(3), in $U_q(sl_2)^{\otimes 3}$ is given in terms of the universal R-matrix of $U_q(sl_2)$. The generators of the centralizer of $U_q(sl_2)$ in its three-fold product…
By requiring invariance directly under the Yangian symmetry, we rederive Beisert's quantum R-matrix, in a form that carries explicit dependence on the representation labels, the braiding factors, and the spectral parameters u_i. In this…
We construct spectral parameter dependent R-matrices for the quantized enveloping algebras of twisted affine Lie algebras. These give new solutions to the spectral parameter dependent quantum Yang-Baxter equation.
R-matrix is explicitly constructed for simplest representations of the Ding-Iohara-Miki algebra. The calculation is straightforward and significantly simpler than the one through the universal R-matrix used for a similar calculation in the…
In this work we use the q-oscillator formalism to construct the atypical (short) supersymmetric representations of the centrally extended Uq (su(2|2)) algebra. We then determine the S-matrix describing the scattering of arbitrary bound…
In this paper we consider solutions to the reflection equation related to the higher spin stochastic six vertex model. The corresponding higher spin $R$-matrix is associated with the affine quantum algebra $U_q(\widehat{sl(2)})$. The…
Recent advances in {matrix-mimetic} tensor frameworks have made it possible to preserve linear algebraic properties for multilinear data analysis and, as a result, to obtain optimal representations of multiway data. Matrix mimeticity arises…
The proposed article aims at offering a comprehensive tutorial for the computational aspects of structured matrix and tensor factorization. Unlike existing tutorials that mainly focus on {\it algorithmic procedures} for a small set of…
In a previous paper the generator matrix elements and (dual) vector reduced Wigner coefficients (RWCs) were evaluated via the polynomial identities satisfied by a certain matrix constructed from the $R$-matrix $R$ and its twisted…
Tensor decompositions have become essential tools for feature extraction and compression of multiway data. Recent advances in tensor operators have enabled desirable properties of standard matrix algebra to be retained for multilinear…
We prove the decomposition of arbitrary diagonal operators into tensor and matrix products of smaller matrices, focusing on the analytic structure of the resulting formulas and their inherent symmetries. Diagrammatic representations are…
Matrix models with continuous symmetry are powerful tools for studying quantum gravity and holography. Tensor models have also found applications in holographic quantum gravity. Matrix models with discrete permutation symmetry have been…
Let g be an affine Lie algebra with associated Yangian Y_hg. We prove the existence of two meromorphic R-matrices associated to any pair of representations of Y_hg in the category O. They are related by a unitary constraint and constructed…
A relation between q-oscillator R-matrix of the tetrahedron equation and decompositions of Poinkare-Birkhoff-Witt type bases for nilpotent subalgebras of U_q(sl_n) is observed.
Motivated by the symmetric version of matrix multiplication we study the plethysm $S^k(\mathfrak{sl}_n)$ of the adjoint representation $\mathfrak{sl}_n$ of the Lie group $SL_n$. In particular, we describe the decomposition of this…
For each simple Lie algebra $\mathfrak{g}$, we construct an algebra embedding of the quantum group $U_q(\mathfrak{g})$ into certain quantum torus algebra $D_\mathfrak{g}$ via the positive representations of split real quantum group. The…
We prove an analogue of the Sylvester theorem for the generator matrices of the quantum affine algebra ${\rm U}_q(\hat{\mathfrak{gl}}_n)$. We then use it to give an explicit realization of the skew representations of the quantum affine…
We discuss the $F$-matrices associated to the $R$-matrix of a general $N$-state vertex model whose statistical configurations encode $N-1$ U(1) symmetries. The factorization condition is shown for arbitrary weights being based only on the…
Quantum superalgebras $su_{q}(m\mid n)$ are studied in the framework of $R$-matrix formalism. Explicit parametrization of $L^{(+)}$ and $L^{(-)}$ matrices in terms of $su_{q}(m\mid n)$ generators are presented. We also show that quantum…
We develop the representation theory of shifted quantum affine algebras $\mathcal{U}_q^\mu(\hat{\mathfrak{g}})$ and of their truncations which appeared in the study of quantized K-theoretic Coulomb branches of 3d $N = 4$ SUSY quiver gauge…