On the irreducible representations of the Lie algebra chain G2⊇A2

Abstract

In the first part of this article we solve the ’’state labelling problem’’ for the irreducible finite dimensional representations of the G2⊆A2 chain, using a method applicable to other algebras-subalgebras chains. In the second part we define, for these representations, operators analogous to those introduced by Nagel and Moshinsky for the An⊆An−1 chain and explicitly construct the representations belonging to two equivalent classes.