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arXiv · 1308.0121

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

N. Aizawa·Y. Kimura·J. Segar
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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.

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N. Aizawa, Y. Kimura, J. Segar. 2013-09-24. Intertwining operators for l-conformal Galilei algebras and hierarchy of invariant equations. https://doi.org/10.1088/1751-8113%2F46%2F40%2F405204

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