Geodesic
The Murnaghan―Nakayama rule for k-Schur functions
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011), DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011) (2011).

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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. 
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     author = {Bandlow, Jason and Schilling, Anne and Zabrocki, Mike},
     title = {The {Murnaghan{\textemdash}Nakayama} rule for {k-Schur} functions},
     journal = {Discrete mathematics & theoretical computer science},
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     volume = {DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011)},
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Bandlow, Jason; Schilling, Anne; Zabrocki, Mike. The Murnaghan―Nakayama rule for k-Schur functions. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011), DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011) (2011). doi : 10.46298/dmtcs.2894. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2894/

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