Jason Bandlow ; Anne Schilling ; Mike Zabrocki - The Murnaghan―Nakayama rule for k-Schur functions

dmtcs:2894 - Discrete Mathematics & Theoretical Computer Science, January 1, 2011, DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011) - https://doi.org/10.46298/dmtcs.2894
The Murnaghan―Nakayama rule for k-Schur functionsArticle

Authors: Jason Bandlow 1; Anne Schilling 2; Mike Zabrocki ORCID3

  • 1 Department of Mathematics [Philadelphia]
  • 2 Department of Mathematics [Univ California Davis]
  • 3 Department of Mathematics and Statistics [Toronto]

We prove a Murnaghan–Nakayama rule for k-Schur functions of Lapointe and Morse. That is, we give an explicit formula for the expansion of the product of a power sum symmetric function and a k-Schur function in terms of k-Schur functions. This is proved using the noncommutative k-Schur functions in terms of the nilCoxeter algebra introduced by Lam and the affine analogue of noncommutative symmetric functions of Fomin and Greene.


Volume: DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011)
Section: Proceedings
Published on: January 1, 2011
Imported on: January 31, 2017
Keywords: Murnaghan―Nayakama rule,symmetric functions,noncommutative symmetric functions,k-Schur functions,[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]
Funding:
    Source : OpenAIRE Graph
  • FRG: Collaborative Research: Affine Schubert Calculus: Combinatorial, geometric, physical, and computational aspects; Funder: National Science Foundation; Code: 0652641
  • 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

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