相关论文: The higher rank $q$-deformed Bannai-Ito and Askey-…
The higher rank Askey-Wilson algebra was recently constructed in the $n$-fold tensor product of $U_q(\mathfrak{sl}_2)$. In this paper we prove a class of identities inside this algebra, which generalize the defining relations of the rank…
The Bannai-Ito algebra $B(n)$ of rank $(n-2)$ is defined as the algebra generated by the Casimir operators arising in the $n$-fold tensor product of the $osp(1,2)$ superalgebra. The structure relations are presented and representations in…
The kernel of the $\mathbb{Z}_2^{n}$ Dirac-Dunkl operator is examined. The symmetry algebra $\mathcal{A}_{n}$ of the associated Dirac-Dunkl equation on $\mathbb{S}^{n-1}$ is determined and is seen to correspond to a higher rank…
An algebra is introduced which can be considered as a rank 2 extension of the Askey-Wilson algebra. Relations in this algebra are motivated by relations between coproducts of twisted primitive elements in the two-fold tensor product of the…
The Dirac-Dunkl operator on the 2-sphere associated to the $\mathbb{Z}_2^3$ reflection group is considered. Its symmetries are found and are shown to generate the Bannai-Ito algebra. Representations of the Bannai-Ito algebra are constructed…
The Gasper and Rahman multivariate $(-q)$-Racah polynomials appear as connection coefficients between bases diagonalizing different abelian subalgebras of the recently defined higher rank $q$-Bannai-Ito algebra $\mathcal{A}_n^q$. Lifting…
The Racah problem for the quantum superalgebra $\mathfrak{osp}_{q}(1|2)$ is considered. The intermediate Casimir operators are shown to realize a $q$-deformation of the Bannai-Ito algebra. The Racah coefficients of $\mathfrak{osp}_q(1|2)$…
The equitable presentation of the quantum superalgebra $\mathfrak{osp}_q(1|2)$, in which all generators appear on an equal footing, is exhibited. It is observed that in their equitable presentations, the quantum algebras…
The $q$-deformation of the infinite-dimensional $n$-algebra is investigated. Based on the structure of the $q$-deformed Virasoro-Witt algebra, we derive a nontrivial $q$-deformed Virasoro-Witt $n$-algebra which is nothing but a sh-$n$-Lie…
In this paper we give a topological interpretation and diagrammatic calculus for the rank $(n-2)$ Askey-Wilson algebra by proving there is an explicit isomorphism with the Kauffman bracket skein algebra of the $(n+1)$-punctured sphere. To…
A one-parameter family of operators that have the complementary Bannai-Ito (CBI) polynomials as eigenfunctions is obtained. The CBI polynomials are the kernel partners of the Bannai-Ito polynomials and also correspond to a $q\rightarrow-1$…
The construction of a q-deformed N=2 superconformal algebra is proposed in terms of level 1 currents of ${\cal{U}}_{q} ({\widehat{su}}(2))$ quantum affine Lie algebra and a single real Fermi field. In particular, it suggests the expression…
An explicit structure relation for Askey-Wilson polynomials is given. This involves a divided q-difference operator which is skew symmetric with respect to the Askey-Wilson inner product and which sends polynomials of degree n to…
A two-variable extension of the Bannai-Ito polynomials is presented. They are obtained via $q\to-1$ limits of the bivariate $q$-Racah and Askey-Wilson orthogonal polynomials introduced by Gasper and Rahman. Their orthogonality relation is…
A quantum superintegrable model with reflections on the $(n-1)$-sphere is presented. Its symmetry algebra is identified with the higher rank generalization of the Bannai-Ito algebra. It is shown that the Hamiltonian of the system can be…
A decomposition of the level-one $q$-deformed Fock representations of $\uqn$ is given. It is found that the action of $\upqn$ on these Fock spaces is centralized by a Heisenberg algebra, which arises from the center of the affine Hecke…
A quantum superintegrable model with reflections on the three-sphere is presented. Its symmetry algebra is identified with the rank-two Bannai-Ito algebra. It is shown that the Hamiltonian of the system can be constructed from the tensor…
n-ary algebras have played important roles in mathematics and mathematical physics. The purpose of this paper is to construct a deformation of Virasoro-Witt n-algebra based on an oscillator realization with two independent parameters (p, q)…
We examine classes of quantum algebras emerging from involutive, non-degenerate set-theoretic solutions of the Yang-Baxter equation and their q-analogues. After providing some universal results on quasi-bialgebras and admissible Drinfeld…
A quantum superintegrable model with reflections on the 2-sphere is introduced. Its two algebraically independent constants of motion generate a central extension of the Bannai--Ito algebra. The Schrodinger equation separates in spherical…