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  1. Home > Articles & Issues >
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  3. The Murnaghan―Nakaya ...
Conference paper

The Murnaghan―Nakayama rule for k-Schur functions

Jason Bandlow (1), Anne Schilling ORCID (2), Mike Zabrocki ORCID (3)
(1) Department of Mathematics [Philadelphia]
(2) Department of Mathematics [Univ California Davis]
(3) Department of Mathematics and Statistics [Toronto]
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Imported on
January 31, 2017
Published on
December 31, 2010
Last modified on
March 31, 2025
Volume
DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011)
Proceedings
DOI
10.46298/dmtcs.2894
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The Murnaghan―Nakayama rule for k-Schur functions

Jason Bandlow (1), Anne Schilling ORCID (2), Mike Zabrocki ORCID (3)
(1) Department of Mathematics [Philadelphia]
(2) Department of Mathematics [Univ California Davis]
(3) Department of Mathematics and Statistics [Toronto]
Abstract
English
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.
French
Nous prouvons une règle de Murnaghan-Nakayama pour les fonctions de k-Schur de Lapointe et Morse, c'est-à-dire que nous donnons une formule explicite pour le développement du produit d'une fonction symétrique "somme de puissances'' et d'une fonction de k-Schur en termes de fonctions k-Schur. Ceci est prouvé en utilisant les fonctions non commutatives k-Schur en termes d'algèbre nilCoxeter introduite par Lam et l'analogue affine des fonctions symétriques non commutatives de Fomin et Greene.
Keywords
  • [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]
  • [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]
  • Murnaghan―Nayakama rule
  • symmetric functions
  • noncommutative symmetric functions
  • k-Schur functions
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