Hermite reciprocity

In mathematics, Hermite's law of reciprocity, introduced by Hermite (1854), 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 it states that the representations S^m Sⁿ C² and Sⁿ S^m C² of GL₂ are isomorphic.

References

Hermite, Charles (1854), "Sur la theorie des fonctions homogenes à deux indéterminées", Cambridge and Dublin Mathematical Journal, 9: 172–217