1204.2871 (Naruhiko Aizawa et al.)

Highest weight representations and Kac determinants for a class of
conformal Galilei algebras with central extension    [PDF]

Naruhiko Aizawa, Phillip S. Isaac, Yuta Kimura

We investigate the representations of a class of conformal Galilei algebras in one spatial dimension with central extension. This is done by explicitly constructing all singular vectors within the Verma modules, proving their completeness and then deducing irreducibility of the associated highest weight quotient modules. A resulting classification of infinite dimensional irreducible modules is presented. It is also shown that a formula for the Kac determinant is deduced from our construction of singular vectors. Thus we prove a conjecture of Dobrev, Doebner and Mrugalla for the case of the Schrodinger algebra.

View original: http://arxiv.org/abs/1204.2871