Geodesic
A new generalization of Hermite's reciprocity law
Journal of Algebraic Combinatorics, Tome 43 (2016) no. 2, pp. 399-416.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Given a partition $\lambda $ of $n$, the Schur functor $\mathbb {S}_\lambda $ associates to any complex vector space $V$, a subspace $\mathbb {S}_\lambda (V)$ of $V^{\otimes n}$. Hermite's reciprocity law, in terms of the Schur functor, states that $\mathbb {S}_{(p)}\left( \mathbb {S}_{(q)}(\mathbb {C}^2)\right) \simeq \mathbb {S}_{(q)}\left( \mathbb {S}_{(p)}(\mathbb {C}^2)\right)$. We extend this identity to many other identities of the type $\mathbb {S}_{\lambda}\left( \mathbb {S}_{\delta}(\mathbb {C}^2)\right) \simeq \mathbb {S}_{\mu}\left( \mathbb {S}_{\epsilon}(\mathbb {C}^2)\right)$.
Classification : 05E05, 05E10
Keywords: Schur functor 
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     title = {A new generalization of {Hermite's} reciprocity law},
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Cagliero, Leandro; Penazzi, Daniel. A new generalization of Hermite's reciprocity law. Journal of Algebraic Combinatorics, Tome 43 (2016) no. 2, pp. 399-416. http://geodesic.mathdoc.fr/item/JAC_2016__43_2_a3/