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The Murnaghan―Nakayama rule for k-Schur functions

Abstract : 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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Jason Bandlow, Anne Schilling, Mike Zabrocki. The Murnaghan―Nakayama rule for k-Schur functions. 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011), 2011, Reykjavik, Iceland. pp.99-110. ⟨hal-01215093⟩

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