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We consider Dunkl version of Laplace-Runge-Lenz vector associated with afinite Coxeter group $W$ acting geometrically in $\mathbb R^N$ withmultiplicity function $g$. This vector generalizes the usual Laplace-Runge-Lenzvector and its components commute with Dunkl-Coulomb Hamiltonian given as DunklLaplacian with additional Coulomb potential $\gamma/r$. We study resultingsymmetry algebra $R_{g, \gamma}(W)$ and show that it hasPoincar\'e-Birkhoff-Witt property. In the absence of Coulomb potential thissymmetry algebra $R_{g,0}(W)$ is a subalgebra of the rational Cherednik algebra$H_g(W)$. We show that a central quotient of the algebra $R_{g, \gamma}(W)$ isa quadratic algebras isomorphic to a central quotient of the correspondingDunkl angular momenta algebra $H_g^{so(N+1)}(W)$. This gives interpretation ofthe algebra $H_g^{so(N+1)}(W)$ as the hidden symmetry algebra of Dunkl-Coulombproblem in $\mathbb R^N$. By specialising $R_{g, \gamma}(W)$ to $g=0$ werecover a quotient of the universal enveloping algebra $U(so(N+1))$ as thehidden symmetry algebra of Coulomb problem in $\mathbb R^N$. We also applyDunkl Laplace-Runge-Lenz vector to establish maximal superintegrability ofgeneralised Calogero-Moser systems.

Algebra of Dunkl Laplace-Runge-Lenz vector