title: Hermite reciprocity
text: # 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 $S^m$ $S^n$ $C^2$ and $S^n$ $S^m$ $C^2$ of $GL_2$ are isomorphic.
  
  