---
tag: 2J9PXE82TJ
kind: concept
name: Isotypical representation
sources:
  - wikipedia: en:40888100@r1354564546
    locator: Isotypical representation
    note: adopted
    mention: wikipedia://en/40888100
    sections: [Summary]
same_as:
  wikidata: Q17043919
  wikipedia: Isotypical representation
inventory: [17JPH8ZQ99]
---

## 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.