Conformal Newton-Hooke symmetry of Pais-Uhlenbeck oscillator

It is demonstrated that the Pais-Uhlenbeck oscillator in arbitrary dimension enjoys the l-conformal Newton-Hooke symmetry provided frequencies of oscillation form the arithmetic sequence ω_k=(2k-1)ω₁, where k=1,…,n, and l is the half-integer 2n-1/2. The model is shown to be maximally superintegrable. A link to n decoupled isotropic oscillators is discussed and an interplay between the l-conformal Newton-Hooke symmetry and symmetries characterizing each individual isotropic oscillator is analyzed.