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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).

05E05 Symmetric functions and generalizations
05E10 Combinatorial aspects of representation theory
14M15 Grassmannians, Schubert varieties, flag manifolds
20C30 Representations of finite symmetric groups
Full Text: DOI arXiv
[1] Bessenrodt C., Kleshchev A.: On Kronecker products of complex representations of the symmetric and alternating groups. Pacific J. Math. 190(2), 201–223 (1999) · Zbl 1009.20013
[2] Sagan B.E.: The Symmetric Group - Representations, Combinatorial Algorithms, and Symmetric Functions, Second Edition. Springer-Verlag, New York (2001) · Zbl 0964.05070
[3] Stembridge J.R.: Multiplicity-Free Products of Schur Functions. Ann. Combin. 5(2), 113–121 (2001) · Zbl 0990.05130
[4] Thomas H., Yong A.: Multiplicity-free Schubert calculus. Canad. Math. Bull. 53, 171–186 (2010) · Zbl 1210.14056
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