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, 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

References

1. Kraft & Procesi, § 1.4. harvnb error: no target: CITEREFKraftProcesi (help)
2. Procesi, Ch 15. § 1.1. harvnb error: no target: CITEREFProcesi (help)

• Claudio Procesi (2007) Lie Groups: an approach through invariants and representation, Springer, ISBN 9780387260402.
• Hanspeter Kraft and Claudio Procesi, Classical Invariant Theory, a Primer