Combinatorial aspects of skew representations of the symmetric group

@article{Garsia1989CombinatorialAO,
  title={Combinatorial aspects of skew representations of the symmetric group},
  author={Adriano M. Garsia and Michelle L. Wachs},
  journal={J. Comb. Theory, Ser. A},
  year={1989},
  volume={50},
  pages={47-81}
}
We give here a very simple combinatorial construction of the skew representations of S,. For the case of hook shapes we give a purely combinatorial proof that our construction does give a representation. In the general case our proof is in terms of A. Young’s natural unifs. One of the biproducts of our construction is an elementary and direct proof of the Murnaghan-Nakayama rule for the character of a general skew representation. ‘c 1989 Academx Press, Inc. 

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