covariant (invariant theory)
In invariant theory, a branch of algebra, given a group G, a covariant is a G-equivariant polynomial map between linear representations V, W of G.{{harvnb|Kraft|Procesi|2016|loc=§ 1.4.}} It is a generalization of a classical convariant,{{clarify|reason=covariant or coinvariant?|date=February 2020}} 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 -equivariant.{{harvnb|Procesi|2007|loc=Ch 15. § 1.1.}}
See also
- Module of covariants
- {{slink|Invariant of a binary form#Terminology}}
- Transvectant{{snd}}method/process of constructing covariants
References
{{reflist}}
- {{cite book | last=Procesi | first=Claudio | title=Lie groups : an approach through invariants and representations | publisher=Springer | publication-place=New York | year=2007 | isbn=978-0-387-26040-2 | oclc=191464530}}
- {{cite web |first1=Hanspeter |last1=Kraft |first2=Claudio |last2=Procesi |url=http://www.math.iitb.ac.in/~shripad/Wilberd/KP-Primer |title=Classical Invariant Theory, a Primer |date=July 2016 |website=Department of Mathematics, IIT Bombay}}
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