Pieri operators on the affine nilCoxeter algebra

@article{Berg2012PieriOO,
  title={Pieri operators on the affine nilCoxeter algebra},
  author={Chris Berg and Franco V. Saliola and Luis G. Serrano},
  journal={arXiv: Combinatorics},
  year={2012}
}
We study a family of operators on the affine nilCoxeter algebra. We use these operators to prove conjectures of Lam, Lapointe, Morse, and Shimozono regarding strong Schur functions. 
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The down operator and expansions of near rectangular k-Schur functions
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