Covariant (invariant theory)

In invariant theory, a branch of algebra, given a group G, a covariant is a G-equivariant polynomial map ${\displaystyle V\to W}$ between linear representations V, W of G.^[1] It is a generalization of a classical convariant,^{[clarification needed]} 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 ${\displaystyle SL_{2}(\mathbb {C} )}$-equivariant.^[2]

See also

• Module of covariants
• Invariant of a binary form § Terminology
• Transvectant – method/process of constructing covariants