# On Reducible Verma Modules over Jacobi Algebra

## TL;DR

This paper initiates the study of reducible Verma modules over the Jacobi algebra, aiming to construct invariant differential operators, and provides initial examples of singular vectors at low levels.

## Contribution

It introduces the analysis of reducible Verma modules over the Jacobi algebra and identifies low-level singular vectors as a step towards invariant differential operators.

## Key findings

- Examples of low-level singular vectors identified
- Methodology for constructing invariant differential operators established
- Foundation laid for further representation theory of Jacobi algebra

## Abstract

With this paper we start the study of reducible representations of the Jacobi algebra with the ultimate goal of constructing differential operators invariant w.r.t. the Jacobi algebra. In this first paper we show examples of the low level singular vectors of Verma modules over the Jacobi algebra. According to our methodology these will produce the invariant differential operators.