Zobrazeno 1 - 10
of 243
pro vyhledávání: '"Bannai-Ito algebra"'
Publikováno v:
Lett. Math. Phys. 113 (2023), no. 5, article number 108
A model of the Bannai-Ito algebra in a superspace is introduced. It is obtained from the three-fold tensor product of the basic realization of the Lie superalgebra $osp(1|2)$ in terms of operators in one continuous and one Grassmanian variable. The b
Externí odkaz:
http://arxiv.org/abs/2306.02714
Autor:
Huang, Hau-Wen
Let $n\geq 0$ denote an integer. Let $\mathscr M_n$ denote the space of Dunkl monogenics of degree $n$ associated with the reflection group $\mathbb Z_2^3$. The universal Bannai--Ito algebra $\mathfrak{BI}$ is a unital associative algebra over $\math
Externí odkaz:
http://arxiv.org/abs/2111.08421
Publikováno v:
J. Phys. A: Math. Theor. 52 (2019) 424001
We provide an explicit isomorphism between a quotient of the Bannai--Ito algebra and the Brauer algebra. We clarify also the connection with the action of the Lie superalgebra osp(1|2) on the threefold tensor product of its fundamental representation
Externí odkaz:
http://arxiv.org/abs/1906.03936
Autor:
De Bie, Hendrik, De Clercq, Hadewijch
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 action o
Externí odkaz:
http://arxiv.org/abs/1902.07883
Autor:
Huang, Hau-Wen
Assume that $\mathbb F$ is an algebraically closed with characteristic $0$. The Bannai--Ito algebra $\mathfrak{BI}$ is a unital associative $\mathbb F$-algebra generated by $X,Y,Z$ and the relations assert that each of \begin{gather*} \{X,Y\}-Z, \qqu
Externí odkaz:
http://arxiv.org/abs/1910.11447
Autor:
De Clercq, Hadewijch
Publikováno v:
SIGMA 15 (2019), 099, 32 pages
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 one Askey-Wi
Externí odkaz:
http://arxiv.org/abs/1908.11654
Autor:
Huang, Hau-Wen
Publikováno v:
SIGMA 16 (2020), 075, 15 pages
Assume that ${\mathbb F}$ is a field with $\operatorname{char}{\mathbb F}\not=2$. The Racah algebra $\Re$ is a unital associative ${\mathbb F}$-algebra defined by generators and relations. The generators are $A$, $B$, $C$, $D$ and the relations asser
Externí odkaz:
http://arxiv.org/abs/1906.11745
The Bannai-Ito algebra can be defined as the centralizer of the coproduct embedding of $\mathfrak{osp}(1|2)$ in $\mathfrak{osp}(1|2)^{\otimes n}$. It will be shown that it is also the commutant of a maximal Abelian subalgebra of $\mathfrak{o}(2n)$ in
Externí odkaz:
http://arxiv.org/abs/1810.00130
An embedding of the Bannai-Ito algebra in the universal enveloping algebra of $\mathfrak{osp}(1,2)$ is provided. A connection with the characterization of the little $-1$ Jacobi polynomials is found in the holomorphic realization of $\mathfrak{osp}(1
Externí odkaz:
http://arxiv.org/abs/1705.09737
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 constructed f
Externí odkaz:
http://arxiv.org/abs/1612.07815