Intertwining operators for l-conformal Galilei algebras and hierarchy of invariant equations

Abstract

l-Conformal Galilei algebra, denoted by g{l}{d}, is a non-semisimple Lie algebra specified by a pair of parameters (d,l). The algebra is regarded as a nonrelativistic analogue of the conformal algebra. We derive hierarchies of partial differential equations which have invariance of the group generated by g{l}{d} with central extension as kinematical symmetry. This is done by developing a representation theory such as Verma modules, singular vectors of g{l}{d} and vector field representations for d = 1, 2.

16pages, version published in J. Phys. A:Math. Theore

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• Quadratic algebras as commutants of algebraic Hamiltonians in the enveloping algebra of Schrödinger algebras
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• The Lie algebra of the lowest transitively differential group of degree three