Covariant (invariant theory)

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.[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 $SL_{2}(\mathbb {C} )$ -equivariant.[2]

See also

module of covariants
Invariant of a binary form#Terminology
Transvectant - method/process of constructing covariants

References

Kraft & Procesi 2016, § 1.4.
Procesi 2007, Ch 15. § 1.1.

Procesi, Claudio (2007). Lie groups : an approach through invariants and representations. New York: Springer. ISBN 978-0-387-26040-2. OCLC 191464530.
Kraft, Hanspeter; Procesi, Claudio (July 2016). "Classical Invariant Theory, a Primer". Department of Mathematics, IIT Bombay.

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