
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. 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.
[info.info-dm] computer science [cs]/discrete mathematics [cs.dm], Affine symmetric group, Affine nilCoxeter algebra, k-Schur functions, Theoretical Computer Science, affine nilCoxeter algebra, Murnaghan-Nakayama rule, QA1-939, FOS: Mathematics, Discrete Mathematics and Combinatorics, Mathematics - Combinatorics, symmetric functions, noncommutative symmetric functions, \(k\)-Schur functions, k-schur functions, cores, [math.math-co] mathematics [math]/combinatorics [math.co], Murnaghan–Nakayama rule, Murnaghan―Nayakama rule, Symmetric functions and generalizations, affine symmetric group, [MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO], Noncommutative symmetric functions, [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM], Computational Theory and Mathematics, Combinatorial aspects of representation theory, Cores, Combinatorics (math.CO), murnaghan―nayakama rule, Mathematics
[info.info-dm] computer science [cs]/discrete mathematics [cs.dm], Affine symmetric group, Affine nilCoxeter algebra, k-Schur functions, Theoretical Computer Science, affine nilCoxeter algebra, Murnaghan-Nakayama rule, QA1-939, FOS: Mathematics, Discrete Mathematics and Combinatorics, Mathematics - Combinatorics, symmetric functions, noncommutative symmetric functions, \(k\)-Schur functions, k-schur functions, cores, [math.math-co] mathematics [math]/combinatorics [math.co], Murnaghan–Nakayama rule, Murnaghan―Nayakama rule, Symmetric functions and generalizations, affine symmetric group, [MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO], Noncommutative symmetric functions, [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM], Computational Theory and Mathematics, Combinatorial aspects of representation theory, Cores, Combinatorics (math.CO), murnaghan―nayakama rule, Mathematics
| selected citations These citations are derived from selected sources. This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically). | 12 | |
| popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network. | Average | |
| influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically). | Top 10% | |
| impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network. | Top 10% |
