Hermite reciprocity: Difference between revisions
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{{short description|Invariant theory in mathematics}} |
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In mathematics, '''Hermite's law of reciprocity''', introduced by {{harvs|txt|last=Hermite|authorlink=Charles Hermite|year=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''<sup>''m''</sup> ''S''<sup>''n''</sup> '''C'''<sup>2</sup> and ''S''<sup>''n''</sup> ''S''<sup>''m''</sup> '''C'''<sup>2</sup> of ''GL''<sub>2</sub> are isomorphic. |
In mathematics, '''Hermite's law of reciprocity''', introduced by {{harvs|txt|last=Hermite|authorlink=Charles Hermite|year=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''<sup>''m''</sup> ''S''<sup>''n''</sup> '''C'''<sup>2</sup> and ''S''<sup>''n''</sup> ''S''<sup>''m''</sup> '''C'''<sup>2</sup> of ''GL''<sub>2</sub> are isomorphic. |
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Revision as of 00:05, 24 September 2020
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 Sm Sn C2 and Sn Sm 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