Abstract : We give a simple characterization of the highest weight vertices in the crystal graph of the level l Fock spaces. This characterization is based on the notion of totally periodic symbols viewed as affine analogues of reverse lattice words classically used in the decomposition of tensor products of fundamental $\mathfrak{sl}_{n}$-modules. This yields a combinatorial decomposition of the Fock spaces in their irreducible components and the branching law for the restriction of the irreducible highest weight $\mathfrak{sl}_{\infty}$-modules to $\widehat{\mathfrak{sl}_{e}}$.
https://hal.archives-ouvertes.fr/hal-00669336
Contributeur : Nicolas Jacon
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Soumis le : lundi 13 février 2012 - 08:42:44
Dernière modification le : mardi 28 août 2018 - 07:48:02
Document(s) archivé(s) le : lundi 14 mai 2012 - 02:21:36
Nicolas Jacon, Cédric Lecouvey. A combinatorial decomposition of higher level Fock spaces. Osaka Journal of Mathematics, Osaka University, 2013, ANR-12-JS01-0003 (3), 18 p. 〈hal-00669336〉
