Séminaire Lotharingien de Combinatoire, 85B.20 (2021), 12 pp.
Cristian Lenart and Adam Schultze
On Combinatorial Models for Affine Crystals
Abstract.
We biject two combinatorial models for tensor products of (single-column) Kirillov-Reshetikhin crystals of any classical type A-D: the quantum alcove model and the tableau model. This allows for the translation of calculations in the former model (of the energy function, the combinatorial R-matrix, the key statistics relevant to Demazure crystals, etc.) to the latter, which is simpler.
Received: December 1, 2020.
Accepted: March 1, 2021.
Final version: April 29, 2021.
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