# Constructions

# Tensor Product

The tensor product of two representations (ρ,V)(\rho,V) and (σ,W)(\sigma,W) of a group GG is the representation (ρσ,VW)(\rho \otimes \sigma, V \otimes W) defined by the condition

(ρσ)(g)(vw):=ρ(g)(v)σ(g)(w),(\rho \otimes \sigma)(g)(v\otimes w) := \rho(g)(v) \otimes \sigma(g) (w),

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