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On Multiplicity-Free Skew Characters and the Schubert Calculus
Christian Gutschwager
Institut für Algebra, Zahlentheorie und Diskrete Mathematik, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, German
Annals of Combinatorics 14 (3) pp.339-353 September, 2010
AMS Subject Classification: 05E05, 05E10, 14M15, 20C30
In this paper we introduce a partial order on the set of skew characters of the symmetric group which we use to classify the multiplicity-free skew characters. Furthermore, we give a short and easy proof that the Schubert
calculus is equivalent to that of skew characters in the following sense: If we decompose the product of two Schubert classes we get the same as if we decompose a skew character and replace the irreducible characters by Schubert classes of the `inverse' partitions (Theorem 4.3).
Keywords: multiplicity-free, skew characters, symmetric group, skew Schur functions, Schubert calculus


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