• 1 Department of Mathematics and Statistics [Albany-USA]

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.