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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
gutschwager@math.uni-hannover.de
Annals of Combinatorics 14 (3) pp.339-353 September, 2010
AMS Subject Classification: 05E05, 05E10, 14M15, 20C30
Abstract:
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

References:

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)

2. Sagan, B.E.: The Symmetric Group - Representations, Combinatorial Algorithms, and Symmetric Functions, Second Edition. Springer-Verlag, New York (2001)

3. Stembridge, J.R.: Multiplicity-Free Products of Schur Functions. Ann. Combin. 5(2), 113--121 (2001)

4. Thomas, H., Yong, A.: Multiplicity-free Schubert calculus. Canad. Math. Bull. 53, 171--186 (2010)