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We split the generic conformal mechanical system into a “radial” and an “angular” part,
where the latter is defined as the Hamiltonian system on the orbit of the conformal group …

A bstract We consider the quantum angular momentum generators, deformed by means of
the Dunkl operators. Together with the reflection operators they generate a subalgebra in …

A bstract We provide a systematic account of integrability of the spherical mechanics
associated with the near horizon extremal Myers-Perry black hole in arbitrary dimension for …

A bstract The rational Calogero-Moser model of n one-dimensional quantum particles with
inverse-square pairwise interactions (in a confining harmonic potential) is reduced along the …

We deform N-dimensional (Euclidean, spherical and hyperbolic) oscillator and Coulomb
systems, replacing their angular degrees of freedom by those of a generalized rational …

A bstract It is long known that the rational Calogero model describing n identical particles on
a line with inverse-square mutual interaction potential is quantum superintegrable. We …

A direct relation is established between the constants of motion for conformal mechanics
and those for its spherical part. In this way, we find the complete set of functionally …

We investigate the matrix-model origin of the spherical sector of the rational Calogero model
and its constants of motion. We develop a diagrammatic technique which allows us to find …

A nonrelativistic particle on a circle and subject to a cos− 2 (kφ) potential is related to the two-
dimensional (dihedral) Coxeter system I2 (k), for k∈ N. For such 'dihedral systems' we …