Covariant (invariant theory)

In the 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.

There is also a more general ring-theoretic notion of covariants; for that, for now, see module of covariants.

See also

• Invariant of a binary form#Terminology
• Transvectant

References

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