Isotypical representation

Summary

In group theory, an isotypical, primary or factor representation of a group G is a unitary representation $\pi : G \longrightarrow \mathcal{B}(\mathcal{H})$ such that any two subrepresentations have equivalent sub-subrepresentations. This is related to the notion of a primary or factor representation of a C*-algebra, or to the factor for a von Neumann algebra: the representation $\pi$ of G is isotypical iff $\pi(G)^{''}$ is a factor.