The Murnaghan-Nakayama rule for k-Schur functions

Abstract

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.

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

References in corpus (2)

• Schubert Polynomials for the affine Grassmannian of the symplectic group
• k-shape poset and branching of k-Schur functions

Cited by in corpus (7)

• $k$-Schur functions and affine Schubert calculus
• Stanley symmetric functions and Peterson algebras
• A Murnaghan-Nakayama rule for Grothendieck polynomials of Grassmannian type
• A generalization of the Murnaghan-Nakayama rule for $K$-$k$-Schur and $k$-Schur functions
• The role of residue and quotient tables in the theory of k-Schur functions
• A quantum Murnaghan--Nakayama rule for the flag manifold
• The down operator and expansions of near rectangular k-Schur functions