Lowest weight representations of super Schrödinger algebras in one dimensional space
Abstract
Lowest weight modules, in particular, Verma modules over the N = 1, 2 super Schrödinger algebras in (1 + 1) dimensional spacetime are investigated. The reducibility of the Verma modules is analyzed via explicitly constructed singular vectors. The classification of the irreducible lowest weight modules is given for both massive and massless representations. A vector field realization of the N = 1, 2 super Schrödinger algebras is also presented.
 Publication:

Journal of Mathematical Physics
 Pub Date:
 January 2011
 DOI:
 10.1063/1.3533920
 arXiv:
 arXiv:1009.0085
 Bibcode:
 2011JMP....52a3509A
 Keywords:

 conformal symmetry;
 Schrodinger equation;
 spacetime configurations;
 supersymmetry;
 vectors;
 03.65.Ge;
 11.30.Ly;
 11.30.Pb;
 02.10.Ud;
 Solutions of wave equations: bound states;
 Other internal and higher symmetries;
 Supersymmetry;
 Linear algebra;
 Mathematical Physics
 EPrint:
 19 pages, no figure