nLab intertwiner

Idea

The term intertwiner is a synonym for homomorphism of representations/actions/modules.

Notably for linear representations $\rho_1$, $\rho_2$ of some group or associative algebra $A$ on vector spaces $V_1, V_2$, a linear map $u : V_1 \to V_2$ is said to intertwine $\rho_1$ with $\rho_2$ if for all $a \in A$ we have that

$$u \circ \rho_1(a) = \rho_2(a)\circ u \,.$$