On irreducible representations of the exotic conformal Galilei algebra

TL;DR

This paper classifies all infinite-dimensional irreducible modules of the exotic conformal Galilei algebra by explicitly constructing singular vectors and analyzing Verma modules.

Contribution

It provides a complete classification of irreducible representations of the exotic conformal Galilei algebra, including explicit construction of singular vectors.

Findings

All singular vectors in Verma modules are explicitly constructed.

Irreducibility of highest weight modules is established.

A comprehensive classification of infinite-dimensional irreducible modules is achieved.

Abstract

We investigate the representations of the exotic conformal Galilei algebra. This is done by explicitly constructing all singular vectors within the Verma modules, and then deducing irreducibility of the associated highest weight quotient modules. A resulting classification of infinite dimensional irreducible modules is presented.