Cristian Lenart ; Anne Schilling - Crystal energy via charge

dmtcs:3015 - 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.3015
Crystal energy via charge

Authors: Cristian Lenart ; Anne Schilling

    The Ram–Yip formula for Macdonald polynomials (at t=0) provides a statistic which we call charge. In types ${A}$ and ${C}$ it can be defined on tensor products of Kashiwara–Nakashima single column crystals. In this paper we show that the charge is equal to the (negative of the) energy function on affine crystals. The algorithm for computing charge is much simpler than the recursive definition of energy in terms of the combinatorial ${R}$-matrix.


    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: affine crystals, energy function, charge, Kashiwara-Nakashima tableaux, Macdonald polynomials,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]
    Fundings :
      Source : OpenAIRE Research Graph
    • FRG: Collaborative Research: Affine Schubert Calculus: Combinatorial, geometric, physical, and computational aspects; Funder: National Science Foundation; Code: 0652652
    • Affine Combinatorics; Funder: National Science Foundation; Code: 1001256
    • Combinatorics of Crystals, Macdonald Polynomials, and Schubert Calculus; Funder: National Science Foundation; Code: 1101264
    • FRG: Collaborative Research: Affine Schubert Calculus: Combinatorial, geometric, physical, and computational aspects; Funder: National Science Foundation; Code: 0652641

    Share

    Consultation statistics

    This page has been seen 132 times.
    This article's PDF has been downloaded 357 times.