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. 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.

See also

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

References

• 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.