Triple Clasp Formulas for $G_2$

TL;DR

This paper provides explicit recursive formulas for projecting onto highest weight irreducible summands in tensor products of fundamental representations of G_2, using Kuperberg's diagrammatic approach.

Contribution

It introduces new recursive formulas for idempotents in G_2 representations based on diagrammatic methods, advancing understanding of their tensor product decompositions.

Findings

Explicit recursive formulas for idempotents in G_2 tensor products

Use of Kuperberg's diagrammatic description for G_2 representations

Enhanced tools for decomposing tensor products of G_2 fundamental representations

Abstract

We use Kuperberg's diagrammatic description of the space of homomorphisms between fundamental representations of $G_2$ to give explicit recursive formulas for the idempotent projecting to the highest weight irreducible summand in each tensor product of fundamental representations.