## Lenart, Cristian and Lubovsky, Arthur - A generalization of the alcove model and its applications

dmtcs:3090 - Discrete Mathematics & Theoretical Computer Science, January 1, 2012, DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012)
A generalization of the alcove model and its applications

Authors: Lenart, Cristian and Lubovsky, Arthur

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.

Volume: DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012)
Section: Proceedings
Published on: January 1, 2012
Submitted on: January 31, 2017
Keywords: energy function,Kirillov-Reshetikhin crystals, alcove model, quantum Bruhat graph, Kashiwara-Nakashima columns,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]