Highest weight representations and Kac determinants for a class of conformal Galilei algebras with central extension
arXiv:1204.2871
Abstract
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.
24 pages
References in corpus (9)
- Toward an AdS/cold atoms correspondence: a geometric realization of the Schroedinger symmetry
- Gravity duals for non-relativistic CFTs
- 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
- Galilean Conformal Algebra in Two Dimensions and Cosmological Topologically Massive Gravity
- Metrics with Galilean Conformal Isometry