In mathematics, Hermite's law of reciprocity, introduced by , states that the degree ''m''
covariants of a binary form of degree ''n'' correspond to the degree ''n'' covariants of a binary form of degree ''m''. In terms of
representation theory
Representation theory is a branch of mathematics that studies abstract algebraic structures by ''representing'' their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures. In essen ...
it states that the representations ''S''
''m'' ''S''
''n'' C
2 and ''S''
''n'' ''S''
''m'' C
2 of ''GL''
2 are isomorphic.
References
*{{Citation , last1=Hermite , first1=Charles , title=Sur la theorie des fonctions homogenes à deux indéterminées , authorlink=Charles Hermite , url=http://resolver.sub.uni-goettingen.de/purl?PPN600493962_0009 , year=1854 , journal=Cambridge and Dublin Mathematical Journal , volume=9 , pages=172–217
Invariant theory