Galilean conformal algebras in two spatial dimension

Abstract

A class of infinite dimensional Galilean conformal algebra in (2+1) dimensional spacetime is studied. Each member of the class, denoted by \alg_{\ell}, is labelled by the parameter \ell. The parameter \ell takes a spin value, i.e., 1/2, 1, 3/2, .... We give a classification of all possible central extensions of \alg_{\ell}. Then we consider the highest weight Verma modules over \alg_{\ell} with the central extensions. For integer \ell we give an explicit formula of Kac determinant. It results immediately that the Verma modules are irreducible for nonvanishing highest weights. It is also shown that the Verma modules are reducible for vanishing highest weights. For half-integer \ell it is shown that all the Verma module is reducible. These results are independent of the central charges.

21 pages, Major revision. Erorr in Theorem 1 is corrected. More general case is investigated. New results, new references

References in corpus (19)

• Toward an AdS/cold atoms correspondence: a geometric realization of the Schroedinger symmetry
• Gravity duals for non-relativistic CFTs
• The BMS/GCA correspondence
• Nonrelativistic conformal field theories
• The flat limit of three dimensional asymptotically anti-de Sitter spacetimes
• BMS/GCA Redux: Towards Flatspace Holography from Non-Relativistic Symmetries
• The geometry of Schrödinger symmetry in non-relativistic CFT
• Acceleration-Extended Galilean Symmetries with Central Charges and their Dynamical Realizations
• (2+1)D Exotic Newton-Hooke Symmetry, Duality and Projective Phase
• On AdS/CFT of Galilean Conformal Field Theories
• Remark on quantum mechanics with conformal Galilean symmetry
• Representations of the Schrödinger-Virasoro algebras
• Galilean Conformal Algebra in Two Dimensions and Cosmological Topologically Massive Gravity
• On nonlinear partial differential equations with an infinite-dimensional conditional symmetry
• Structure of the extended Schrodinger-Virasoro Lie algebra
• W-algebra W(2,2) and the vertex operator algebra L(1/2,0)\otimes L(1/2,0)
• The derivations, central extensions and automorphism group of the Lie algebra $W$
• Automorphisms and Verma modules for Generalized Schrödinger-Virasoro algebras
• Some representations of planar Galilean conformal algebra

Cited by in corpus (6)

• Dynamical realization of l-conformal Galilei algebra and oscillators
• On dynamical realizations of l-conformal Galilei groups
• The (super)conformal BMS${}_3$ algebra
• N=2 supersymmetric extension of l-conformal Galilei algebra
• Some representations of planar Galilean conformal algebra
• Remarks on BMS${}_3$ invariant field theories: correlation functions and nonunitary CFTs