Zobrazeno 1 - 10
of 49
pro vyhledávání: '"Oste, Roy"'
The Dunkl deformation of the Dirac operator is part of a realisation of an orthosymplectic Lie superalgebra inside the tensor product of a rational Cherednik algebra and a Clifford algebra. The Dunkl total angular momentum algebra (TAMA) occurs as th
Externí odkaz:
http://arxiv.org/abs/2308.16366
For a finite dimensional representation $V$ of a finite reflection group $W$, we consider the rational Cherednik algebra $\mathsf{H}_{t,c}(V,W)$ associated with $(V,W)$ at the parameters $t\neq 0$ and $c$. The Dunkl total angular momentum algebra $O_
Externí odkaz:
http://arxiv.org/abs/2207.11185
Publikováno v:
In Journal of Algebra 15 November 2024 658:198-226
Publikováno v:
Rocky Mountain J. Math. 53 (2) 397-415 (2023)
We introduce a family of commuting generalised symmetries of the Dunkl--Dirac operator inspired by the Maxwell construction in harmonic analysis. We use these generalised symmetries to construct bases of the polynomial null-solutions of the Dunkl--Di
Externí odkaz:
http://arxiv.org/abs/2203.01204
Autor:
Oste, Roy
In recent work, we examined the algebraic structure underlying a class of elements supercommuting with realization of the Lie superalgebra $\mathfrak{osp}(1|2)$ inside a generalization of the Weyl Clifford algebra. This generalization contained in pa
Externí odkaz:
http://arxiv.org/abs/2110.15337
The Dunkl--Dirac operator is a deformation of the Dirac operator by means of Dunkl derivatives. We investigate the symmetry algebra generated by the elements supercommuting with the Dunkl--Dirac operator and its dual symbol. This symmetry algebra is
Externí odkaz:
http://arxiv.org/abs/2010.03381
Autor:
Langlois-Rémillard, Alexis, Oste, Roy
We initiate the study of an algebra of symmetries for the 3D Dirac-Dunkl operator associated with the Weyl group of the exceptional root system $G_2$. For this symmetry algebra, we give both an abstract definition and an explicit realisation. We then
Externí odkaz:
http://arxiv.org/abs/2009.13904
We study deformations of the Howe dual pairs $(\mathrm{U}(n),\mathfrak{u}(1,1))$ and $(\mathrm{U}(n),\mathfrak{u}(2|1))$ to the context of a rational Cherednik algebra $H_{1,c}(G,E)$ associated with a real reflection group $G$ acting on a real vector
Externí odkaz:
http://arxiv.org/abs/2009.05412
Publikováno v:
Annals of Physics 389 (2018) 192-218
We consider the symmetry algebra generated by the total angular momentum operators, appearing as constants of motion of the $\mathrm{S}_3$ Dunkl Dirac equation. The latter is a deformation of the Dirac equation by means of Dunkl operators, in our cas
Externí odkaz:
http://arxiv.org/abs/1705.08751
Publikováno v:
Lett. Math. Phys. 108 (2018), 1905-1953
We consider a generalization of the classical Laplace operator, which includes the Laplace-Dunkl operator defined in terms of the differential-difference operators associated with finite reflection groups called Dunkl operators. For this Laplace-like
Externí odkaz:
http://arxiv.org/abs/1701.05760