A generalization of the alcove model and its applications

Details A generalization of the alcove model and its applications A generalization of the alcove model and its applications

2011-12-09

arxiv.org/abs/1112.2216v1

Mathematics

Combinatorics

Scientific paper

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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