Singlets in the tensor product of an arbitrary number of Adjoint representations of SU(3)

TL;DR

This paper introduces recurrence relations to efficiently compute the number of invariants in tensor products of multiple adjoint representations of SU(3), aiding in understanding the structure of these tensor products.

Contribution

The paper presents a novel set of four recurrence relations that determine the dimension of invariant subspaces in tensor products of SU(3) adjoint representations.

Findings

Recurrence relations accurately compute invariants for any number of tensor factors.

The method simplifies calculations of invariants in complex tensor products.

Provides a systematic approach to understanding SU(3) invariants.

Abstract

We propose a set of 4 recurrence relations whose linear combination gives the number of group invariants, equivalently the dimension of the invariant subspace, in the tensor product of an arbitrary number of adjoint representations of the SU(3) Lie Group.