Some representations of planar Galilean conformal algebra

2012/12/27 by N. Aizawa, Aizawa, N.
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph)

paper · pdf · doi:10.48550/arxiv.1212.6288

openalex publication_date 2012/12/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Cited by

• Galilean conformal algebras in two spatial dimension

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