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- W2584863178 abstract "The alcove model of the first author and Postnikov describes highest weight crystals of semisimple Lie algebras. We present a generalization, called the quantum alcove model, and conjecture that it uniformly describes tensor products of column shape Kirillov-Reshetikhin crystals, for all untwisted affine types. We prove the conjecture in types $A$ and $C$. We also present evidence for the fact that a related statistic computes the energy function. Le modèle des alcôves du premier auteur et Postnikov décrit les cristaux de plus haut poids des algèbres de Lie semi-simples. Nous présentons une généralisation, appelée le modèle des alcôves quantique, et nous conjecturons qu’il décrit dans une manière uniforme les produits tensoriels des cristaux de Kirillov-Reshetikhin de type colonne, pour toutes les types affines symétriques. Nous prouvons la conjecture dans les types $A$ et $C$. Nous fournissons aussi des preuves qu’une statistique associée donne la fonction d’énergie." @default.
- W2584863178 created "2017-02-10" @default.
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- W2584863178 date "2012-01-01" @default.
- W2584863178 modified "2023-10-14" @default.
- W2584863178 title "A generalization of the alcove model and its applications" @default.
- W2584863178 doi "https://doi.org/10.46298/dmtcs.3090" @default.
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