DMTCS Proceedings, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012)

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A generalization of the alcove model and its applications

Cristian Lenart, Arthur Lubovsky


 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.

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