---
tag: 8WA2DAG5P7
kind: concept
name: Covariant (invariant theory)
sources:
  - wikipedia: en:61740916@r1336929947
    locator: Covariant (invariant theory)
    note: adopted
    mention: wikipedia://en/61740916
    sections: [Summary]
same_as:
  wikidata: Q85754410
  wikipedia: Covariant (invariant theory)
inventory: [D2NQ6DE9RK]
---

## Summary

In invariant theory, a branch of algebra, given a group *G*, a **covariant** is a *G*-equivariant polynomial map $V \to W$ between linear representations *V*, *W* of *G*. It is a generalization of a classical convariant, which is a homogeneous polynomial map from the space of binary *m*-forms to the space of binary *p*-forms (over the complex numbers) that is $SL_2(\mathbb{C})$-equivariant.