Weyl's construction and tensor power decomposition for $G_{2}$

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 $G_{2}$.