Tensor product of group representations

Given two representations $𝔛 : 𝐺 \to G L (𝑉)$ and $𝔜 : 𝐺 \to G L (𝑊)$ , the tensor product $𝔛 \otimes 𝔜 : 𝐺 \to G L (V \otimes W)$ is defined using the $K$ -tensor product of linear maps as

(𝔛 \otimes 𝔜) (𝐺) = 𝔛 (𝐺) \otimes 𝔜 (𝐺)

We denote the tensor product of irreps as $𝔛 𝜇 \otimes 𝔛 𝜈 = 𝔛 𝜇 \otimes 𝜈$

Tensor product of group representations

See also