The Murnaghan-Nakayama rule for k-Schur functions

Details The Murnaghan-Nakayama rule for k-Schur functions The Murnaghan-Nakayama rule for k-Schur functions

2010-04-27

arxiv.org/abs/1004.4886v2

Journal of Combinatorial Theory, Series A, 118(5) (2011) 1588-1607

Mathematics

Combinatorics

23 pages, updated to reflect referee comments, to appear in Journal of Combinatorial Theory, Series A

Scientific paper

10.1016/j.jcta.2011.01.009

We prove the Murgnaghan--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.

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