Cristian Lenart ; Arthur Lubovsky
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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)
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https://doi.org/10.46298/dmtcs.3090
A generalization of the alcove model and its applications
Authors: Cristian Lenart 1; Arthur Lubovsky 1
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Cristian Lenart;Arthur Lubovsky
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.
On crystal bases of the $Q$-analogue of universal enveloping algebras
2 Documents citing this article
Source : OpenCitations
Lenart, Cristian, 2012, From Macdonald Polynomials To A Charge Statistic Beyond Type A, Journal Of Combinatorial Theory, Series A, 119, 3, pp. 683-712, 10.1016/j.jcta.2011.11.013.
Lenart, Cristian; Schilling, Anne, 2012, Crystal Energy Functions Via The Charge In Types A And C, Mathematische Zeitschrift, 273, 1-2, pp. 401-426, 10.1007/s00209-012-1011-2.