# # Constructions

## # Tensor Product

The tensor product of two representations $(\rho,V)$ and $(\sigma,W)$ of a group $G$ is the representation $(\rho \otimes \sigma, V \otimes W)$ defined by the condition

$(\rho \otimes \sigma)(g)(v\otimes w) := \rho(g)(v) \otimes \sigma(g) (w),$

and extended to all vectors in $V \otimes W$ by linearity.

Last Updated: 12/17/2019, 6:02:45 AM