# Lowest weight representations of super Schrödinger algebras in one dimensional space

@article{Aizawa2011LowestWR, title={Lowest weight representations of super Schr{\"o}dinger algebras in one dimensional space}, author={Naruhiko Aizawa}, journal={Journal of Mathematical Physics}, year={2011}, volume={52}, pages={013509} }

Lowest weight modules, in particular, Verma modules over the N=1,2 super Schrodinger 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 Schrodinger algebras is also presented.

## 7 Citations

Lowest weight representations of super Schrödinger algebras in low dimensional spacetime

- Mathematics, Physics
- 2010

We investigate the lowest weight representations of the super Schrodinger algebras introduced by Duval and Horvathy. This is done by the same procedure as the semisimple Lie algebras. Namely, all…

Simple Harish-Chandra supermodules over the super Schrödinger algebra

- Mathematics
- 2015

We study the N = 1 super Schrödinger algebra S in (1 + 1)-dimensional spacetime. The first part of this paper determines the necessary and sufficient conditions for highest weight supermodules over S…

Simple Harish-Chandra modules over super Schrödinger algebra in (1+1) dimensional spacetime

- Mathematics
- 2014

The N = 1 super Schrodinger algebra S(1|1) in (1+1) dimensional spacetime contains a subalgebra isomorphic to osp(1|2)-module. Let V be a simple weight module for the N = 1 super Schrodinger algebra…

Extremal vectors for Verma type factor-representations of U q ( sl (3, ℂ))

- Physics
- 2012

To analyze the reducibility of the Verma modules one often needs to find the extremal vectors of the given representations. On the example of algebra Uq(sl(3, ℂ)) we study how the set of extremal…

N = 2 Galilean superconformal algebras with central extension

- Physics, Mathematics
- 2012

N = 2 Supersymmetric extensions of Galilean conformal algebra (GCA), specified by spin \ell and dimension of space d, are investigated. Duval and Horvathy showed that the \ell = 1/2 GCA has two types…

NONRELATIVISTIC HOLOGRAPHY — A GROUP-THEORETICAL PERSPECTIVE

- Physics, Mathematics
- 2014

We give a review of some group-theoretical results related to nonrelativistic holography. Our main playgrounds are the Schrodinger equation and the Schrodinger algebra. We first recall the…

A Complete Bibliography of Publications in the Journal of Mathematical Physics: 2005{2009

- Computer Science, Mathematics
- 2015

(2 < p < 4) [200]. (Uq(∫u(1, 1)), oq1/2(2n)) [92]. 1 [273, 79, 304, 119]. 1 + 1 [252]. 2 [352, 318, 226, 40, 233, 157, 299, 60]. 2× 2 [185]. 3 [456, 363, 58, 18, 351]. ∗ [238]. 2 [277]. 3 [350]. p…

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