Sunday, August 4, 2013

1308.0121 (N. Aizawa et al.)

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

N. Aizawa, Y. Kimura, J. Segar
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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