### arXiv:1212.6288 [math-ph]AbstractReferencesReviewsResources

#### Some representations of planar Galilean conformal algebra

Published 2012-12-27, updated 2013-01-04Version 2

Representation theory of an infinite dimensional Galilean conformal algebra introduced by Martelli and Tachikawa is developed. We focus on the algebra defined in (2+1) dimensional spacetime and consider central extension. It is then shown that the Verma modules are irreducible for non-vanishing highest weights. This is done by explicit computation of Kac determinant. We also present coadjoint representations of the Galilean conformal algebra and its Lie group. As an application of them, a coadjoint orbit of the Galilean conformal group is given in a simple case.

**Comments:**10 pages. Talk given at 7th Mathematical Physics Meeting: Summer School and Conference on Modern Mathematical Physics, September 2012, Belgrade, Serbia, reference added

**Keywords:**planar galilean conformal algebra, infinite dimensional galilean conformal algebra, galilean conformal group, central extension, representation theory

**Tags:**conference paper

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