Zobrazeno 1 - 10
of 163
pro vyhledávání: '"Genest, Vincent X."'
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
Generalizations of the (rank 1) Bannai-Ito algebra are obtained from a refinement of the grade involution of the Lie super algebra $\mathfrak{osp}(1,2)$. A hyperoctahedral extension is derived by using a realization of $\mathfrak{osp}(1,2)$ in terms
Externí odkaz:
http://arxiv.org/abs/1705.03761
We study 1+1 dimensional $\phi^4$ theory using the recently proposed method of conformal truncation. Starting in the UV CFT of free field theory, we construct a complete basis of states with definite conformal Casimir, $\mathcal{C}$. We use these sta
Externí odkaz:
http://arxiv.org/abs/1704.04500
Publikováno v:
Nuclear Phys. B 927 (2018), 97--123
Gasper & Rahman's multivariate $q$-Racah polynomials are shown to arise as connection coefficients between families of multivariate $q$-Hahn or $q$-Jacobi polynomials. The families of $q$-Hahn polynomials are constructed as nested Clebsch--Gordan coe
Externí odkaz:
http://arxiv.org/abs/1702.04626
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
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 bases deter
Externí odkaz:
http://arxiv.org/abs/1610.04797
Publikováno v:
J. Phys. A: Math. Theor. 51 (2018) 025203
A higher rank generalization of the (rank one) Racah algebra is obtained as the symmetry algebra of the Laplace-Dunkl operator associated to the $\mathbb{Z}_2^n$ root system. This algebra is also the invariance algebra of the generic superintegrable
Externí odkaz:
http://arxiv.org/abs/1610.02638
The quantum rotor is shown to be supersymmetric. The supercharge $Q$, whose square equals the Hamiltonian, is constructed with reflection operators. The conserved quantities that commute with $Q$ form the algebra $so(3)_{-1}$, an anticommutator versi
Externí odkaz:
http://arxiv.org/abs/1607.06967
Persymmetric Jacobi matrices are invariant under reflection with respect to the anti-diagonal. The associated orthogonal polynomials have distinctive properties that are discussed. They are found in particular to be also orthogonal on the restriction
Externí odkaz:
http://arxiv.org/abs/1605.00708
Publikováno v:
Acta Polytechnica (2016) 56
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 product of f
Externí odkaz:
http://arxiv.org/abs/1601.07642