A new generalization of Hermite's reciprocity law

LEANDRO CAGLIERO; DANIEL PENAZZI

JOURNAL OF ALGEBRAIC COMBINATORICS

SPRINGER

Lugar: Berlin; Año: 2016 vol. 43 p. 399 - 416

0925-9899

Given a partition $\lambda$ of $n$, the {\it 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 $\mathbb{S}_{\lambda}\left(\mathbb{S}_{\delta}(\mathbb{C}^2)\right)\simeq \mathbb{S}_{\mu}\left(\mathbb{S}_{\epsilon}(\mathbb{C}^2)\right)$.