Related papers: Central elements for quantum affine algebras and a…
In this paper, the complete description of centralizers of elements in partially commutative Lie algebras is obtained. The description is given explicitly in the terms of generators.
We study the quantum symmetric spaces for quantum general linear groups modulo symplectic groups. We first determine the structure of the quotient quantum group and completely determine the quantum invariants. We then derive the…
We propose a list of inequalities which characterize central elements in von Neumann algebras and C*-algebras.
We define the notion of a (linearly reductive) center for a linearly reductive quantum group, and show that the quotient of a such a quantum group by its center is simple whenever its fusion semiring is free in the sense of Banica and…
Let $(\mathbf{U}, \mathbf{U}^\imath)$ be a split affine quantum symmetric pair of type $\mathsf{B}_n^{(1)}, \mathsf{C}_n^{(1)}$ or $\mathsf{D}_n^{(1)}$. We prove factorization and coproduct formulae for the Drinfeld-Cartan operators…
We describe a connection between the subjects of cluster algebras, polynomial identity algebras and discriminants. For this, we define the notion of root of unity quantum cluster algebras and prove that they are polynomial identity…
All algebras in a very large, axiomatically defined class of quantum nilpotent algebras are proved to possess quantum cluster algebra structures under mild conditions. Furthermore, it is shown that these quantum cluster algebras always…
We propose models of quantum neural networks through Clifford algebras, which are capable of capturing geometric features of systems and to produce entanglement. Due to their representations in terms of Pauli matrices, the Clifford algebras…
We construct special solutions of the quantum Knizhnik-Zamolodchikov equation on the tensor product of the vector representation of the quantum algebra of type A_{N-1}. They are constructed from non-symmetric Macdonald polynomials through…
We apply the theory of $\phi$-coordinated modules, developed by H.-S. Li, to the Etingof--Kazhdan quantum affine vertex algebra associated with the trigonometric $R$-matrix of type $A$. We prove, for a certain associate $\phi$ of the…
We study evaluation modules for quantum symmetric pair coideal subalgebras of affine type $\mathsf{AI}$. By computing the action of the generators in Lu and Wang's Drinfeld-type presentation on Gelfand-Tsetlin bases, we determine the…
The present work shows that magnetic quivers encode the necessary information for determining the Drinfeld center in the symmetry topological field theory constructions (SymTFT) associated to a given absolute theory. The crucial argument…
Many possible definitions have been proposed for fractional derivatives and integrals, starting from the classical Riemann-Liouville formula and its generalisations and modifying it by replacing the power function kernel with other kernel…
In this paper, we extend the Drinfeld current realization of quantum affine algebras $U_q(\hat {\gg})$ and of the Yangians in several directions: we construct current operators for non-simple roots of ${\gg}$, define a new braid group…
We consider principal subspace W({\Lambda}) of integrable highest weight module L({\Lambda}) for quantum affine algebra $U_q(\hat{\mathfrak{sl}}_{n+1})$. We introduce quantum analogues of the quasi-particles associated with the principal…
In this paper, we study the fractional decomposition of the quantum enveloping affine algebras $U_Q(\hat A(n))$ and $U_Q(\hat{C}(n))$ with vanishing central charge in the limit $Q\to q=e^{\frac{2i\pi}k}$ . This decomposition is based on the…
We define a new $q$-deformation of Brauer's centralizer algebra which contains Hecke algebras of type $A$ as unital subalgebras. We determine its generic structure as well as the structure of certain semisimple quotients. This is expected…
It is known that the universal enveloping algebra of the orthogonal Lie algebra of size even has a central element expressed in terms of Pfaffian of a certain matrix alternating along the anti-diagonal (which we call anti-alternating for…
A method to calculate matrix representations of the twist element $\ff$ of Drinfel'd -- chosen to be unitary -- is given and illustrated at some examples. It is observed that for these F-matrices the crystal limit $q\!\to\! 0$ exists and…
The quantum affine $\CU_q (\hat{sl(2)}) $ symmetry is studied when $q^2$ is an even root of unity. The structure of this algebra allows a natural generalization of N=2 supersymmetry algebra. In particular it is found that the momentum…