We introduce Dunkl version of Laplace-Runge-Lenz vector associated with a
finite Coxeter group $W$ acting geometrically in $\mathbb R^N$ with
multiplicity function $g$. This vector commutes with Dunkl Laplacian with
additional Coulomb potential $\gamma/r$, and it generalises the usual
Laplace-Runge-Lenz vector. We study resulting symmetry algebra $R_{g,
\gamma}(W)$ and show that it has Poincar\'e-Birkhoff-Witt property. In the
absence of Coulomb potential this symmetry algebra is a subalgebra of the
rational Cherednik algebra $H_g(W)\supset R_{g,0}(W)$. We show that its central
quotient is a quadratic algebra isomorphic to a central quotient of the
corresponding Dunkl angular momenta algebra $H_g^{so(N+1)}(W)$. This gives
interpretation of the algebra $H_g^{so(N+1)}(W)$ as the hidden symmetry algebra
of Dunkl Laplacian. On the other hand by specialising $R_{g, \gamma}(W)$ to
$g=0$ we recover a quotient of the universal enveloping algebra $U(so(N+1))$ as
the hidden symmetry algebra of Coulomb problem in ${\mathbb R}^N$.

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adhara_mathphys:
RT @SciencePapers: Algebra of Dunkl Laplace-Runge-Lenz vector. https://t.co/YZTv8dLJ2D

adhara_mathphys:
RT @SciencePapers: Algebra of Dunkl Laplace-Runge-Lenz vector. https://t.co/YZTv8dLJ2D

YosukeSaito7:
RT @mathQAb: Misha Feigin, Tigran Hakobyan : Algebra of Dunkl Laplace-Runge-Lenz vector https://t.co/7gN49CmMAt https://t.co/OGqX0YJoGU

mathQAb:
Misha Feigin, Tigran Hakobyan : Algebra of Dunkl Laplace-Runge-Lenz vector https://t.co/7gN49CmMAt https://t.co/OGqX0YJoGU

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Misha Feigin, Tigran Hakobyan : Algebra of Dunkl Laplace-Runge-Lenz vector https://t.co/EMw7VmKq6q https://t.co/VuZ1ryoMxz

SciencePapers:
Algebra of Dunkl Laplace-Runge-Lenz vector. https://t.co/YZTv8dLJ2D