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The Murnaghan-Nakayama rule for k-Schur functions |
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| Authors: | Jason Bandlow Anne Schilling Mike Zabrocki |
| Institution: | a Department of Mathematics, University of Pennsylvania, David Rittenhouse Laboratory, 209 South 33rd Street, Philadelphia, PA 19104-6395, USA b Department of Mathematics, One Shields Avenue, University of California, Davis, CA 95616, USA c York University, Mathematics and Statistics, 4700 Keele Street, Toronto, Ontario M3J 1P3, Canada |
| Abstract: | We prove the 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. |
| Keywords: | Noncommutative symmetric functions Murnaghan-Nakayama rule k-Schur functions Affine symmetric group Affine nilCoxeter algebra Cores |
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