Weyl’s construction and tensor power decomposition for 𝐺₂

Huang, Jing-Song; Zhu, Chen-Bo

doi:10.1090/S0002-9939-99-04583-9

Weyl’s construction and tensor power decomposition for $G_2$
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by Jing-Song Huang and Chen-Bo Zhu

Proc. Amer. Math. Soc. 127 (1999), 925-934

DOI: https://doi.org/10.1090/S0002-9939-99-04583-9

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Abstract:

Let $V$ be the 7-dimensional irreducible representations of $G_{2}$. We decompose the tensor power $V^{\otimes n}$ into irreducible representations of $G_{2}$ and obtain all irreducible representations of $G_{2}$ 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 $G_{2}$.

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