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 chargeArticle

Authors: Cristian Lenart 1; Anne Schilling 2

  • 1 Department of Mathematics and Statistics [Albany-USA]
  • 2 Department of Mathematics [Univ California Davis]

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]
Funding:
    Source : OpenAIRE Graph
  • Affine Combinatorics; Funder: National Science Foundation; Code: 1001256
  • FRG: Collaborative Research: Affine Schubert Calculus: Combinatorial, geometric, physical, and computational aspects; Funder: National Science Foundation; Code: 0652641
  • 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: 0652652

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