Weyl’s construction and tensor power decomposition for 𝐺₂

Abstract

Let V V be the 7-dimensional irreducible representations of G 2 G_{2} . We decompose the tensor power V ⊗ n V^{\otimes n} into irreducible representations of G 2 G_{2} and obtain all irreducible representations of G 2 G_{2} in the decomposition. This generalizes Weyl’s work on the construction of irreducible representations and decomposition of tensor products for classical groups to the exceptional group G 2 G_{2} .