Classification of finite dimensional uniserial representations of conformal Galilei algebras

TL;DR

This paper classifies all uniserial modules of certain Lie algebras using the 6j-symbol, providing a complete understanding of their structure in the context of conformal Galilei algebras.

Contribution

It introduces a classification method for uniserial modules of semidirect product Lie algebras using the 6j-symbol, a novel approach in this area.

Findings

Complete classification of uniserial modules for the specified Lie algebras

Application of the 6j-symbol in module classification

Insight into the structure of conformal Galilei algebra representations

Abstract

With the aid of the $6j$-symbol, we classify all uniserial modules of $\mathfrak{sl}(2)\ltimes \mathfrak{h}_{n}$, where $\mathfrak{h}_{n}$ is the Heisenberg Lie algebra of dimension $2n+1$.