10,827 research outputs found
On irreducible representations of the exotic conformal Galilei algebra
We investigate the representations of the exotic conformal Galilei algebra.
This is done by explicitly constructing all singular vectors within the Verma
modules, and then deducing irreducibility of the associated highest weight
quotient modules. A resulting classification of infinite dimensional
irreducible modules is presented.Comment: 11 pages, added 6 references and conclusing remark
On realizations of polynomial algebras with three generators via deformed oscillator algebras
We present the most general polynomial Lie algebra generated by a second
order integral of motion and one of order M, construct the Casimir operator,
and show how the Jacobi identity provides the existence of a realization in
terms of deformed oscillator algebra. We also present the classical analog of
this construction for the most general Polynomial Poisson algebra. Two specific
classes of such polynomial algebras are discussed that include the symmetry
algebras observed for various 2D superintegrable systems.Comment: 28 page
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