Cristian Lenart ; Arthur Lubovsky - 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) - https://doi.org/10.46298/dmtcs.3090
A generalization of the alcove model and its applications

Authors: Cristian Lenart ; Arthur Lubovsky

    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
    Imported 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]
    Fundings :
      Source : OpenAIRE Research Graph
    • Combinatorics of Crystals, Macdonald Polynomials, and Schubert Calculus; Funder: National Science Foundation; Code: 1101264

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    Source : ScholeXplorer IsReferencedBy DOI 10.1007/s10468-019-09904-5
    • 10.1007/s10468-019-09904-5
    • 10.1007/s10468-019-09904-5
    • 10.1007/s10468-019-09904-5
    Kirillov–Reshetikhin Crystals B1, s for ̂ n $\widehat {\mathfrak {s}\mathfrak {l}}_{n}$ Using Nakajima Monomials
    Gunawan, Emily ; Scrimshaw, Travis ;

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