Jennifer Morse ; Anne Schilling - Affine charge and the $k$-bounded Pieri rule

dmtcs:2470 - Discrete Mathematics & Theoretical Computer Science, January 1, 2015, DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015) - https://doi.org/10.46298/dmtcs.2470
Affine charge and the $k$-bounded Pieri ruleArticle

Authors: Jennifer Morse 1; Anne Schilling 2

  • 1 Department of mathematics [Philadelphie]
  • 2 Department of Mathematics [Univ California Davis]

We provide a new description of the Pieri rule of the homology of the affine Grassmannian and an affineanalogue of the charge statistics in terms of bounded partitions. This makes it possible to extend the formulation ofthe Kostka–Foulkes polynomials in terms of solvable lattice models by Nakayashiki and Yamada to the affine setting.


Volume: DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015)
Section: Proceedings
Published on: January 1, 2015
Imported on: November 21, 2016
Keywords: affine Schubert calculus,Charge statistic,Pieri rule,$k$-Schur functions,energy function,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]
Funding:
    Source : OpenAIRE Graph
  • Combinatorics in algebra, geometry, and physics; Funder: National Science Foundation; Code: 1301695
  • Collaborative Research: SI2-SSE: Sage-Combinat: Developing and Sharing Open Source Software for Algebraic Combinatorics; Funder: National Science Foundation; Code: 1147247

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