Invariant partial differential equations with two-dimensional exotic centrally extended conformal Galilei symmetry (Q2804960)

This paper presents an interesting addition to the construction of dynamical systems invariant with respect to (centrally extended) conformal Galilei algebras. Specifically, it is shown that for the case of \(d=2\) exotic centrally extended conformal Galilei algebras there exists an associated second-order invariant partial differential equation (PDE), the spectrum of which is bounded and discrete when applied to lowest weight representations of the algebra. This case finishes the analysis of PDEs possessing a discrete spectrum. It should be observed that the properties of this extension radically differ from those observed for the usual central extensions, as obtained by the authors in [J. Math. Phys. 56, No. 3, 031701, 14 p. (2015; Zbl 1319.81030)].