Classification of the Reducible Verma Modules over the Jacobi Algebra G2

In the present paper we study representations of Jacobi algebra. More concretely, define, analogously to case semi-simple Lie algebras, Verma modules over algebra ${\cal G}_2$. We their reducibility and give explicit construction reducible exhibiting corresponding singular vectors. Using this information a complete classification modules. than exhibit interrelation embeddings between these These are illustrated by diagrams embedding patterns so that each module appears in one such diagram.