# Resolution of SU(3) Outer Multiplicity Problem and the $SU(3)\otimes SU(3)$ Invariant Group $SO(4,2)$

## TL;DR

This paper addresses the SU(3) outer multiplicity problem by identifying invariant operators forming an SO(4,2) algebra, enabling the distinction of repeated representations in SU(3) tensor products.

## Contribution

It introduces a method to resolve the SU(3) outer multiplicity problem using SO(4,2) invariant operators constructed from SU(3) Schwinger bosons.

## Key findings

- Invariant operators form SO(4,2) algebra
- Constructed operators distinguish repeated representations
- Provides a systematic approach to multiplicity resolution

## Abstract

We resolve the SU(3) outer multiplicity problem by defining all possible $SU(3)\otimes SU(3)$ invariant operators in terms of SU(3) Schwinger bosons. We show that the elementary invariant operators relevant to the outer multiplicity problem form SO(4,2) algebra. Further, they enable us to construct a family of operators any one of which can be used to distinguish repeating representations present in the reduction of the direct product of two SU(3) irreducible representations.