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On multiplicity-free skew characters and the Schubert calculus. (English) Zbl 1233.05201
Summary: 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).

MSC:
05E05 Symmetric functions and generalizations
05E10 Combinatorial aspects of representation theory
14M15 Grassmannians, Schubert varieties, flag manifolds
20C30 Representations of finite symmetric groups
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References:
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