Equality of multiplicity free skew characters
Christian Gutschwager
DOI: 10.1007/s10801-008-0158-8
Abstract
In this paper we show that two skew diagrams λ / μ and α / β can represent the same multiplicity free skew character [ λ / μ ]=[ α / β ] only in the the trivial cases when λ / μ and α / β are the same up to translation or rotation or if λ = α is a staircase partition λ =( l, l - 1,\cdots ,2,1) and λ / μ and α / β are conjugate of each other.
Pages: 215–232
Keywords: keywords skew characters; symmetric group; skew Schur functions; Schubert calculus
Full Text: PDF
References
1. Gutschwager, C.: On multiplicity-free skew characters and the Schubert Calculus. Annals Comb. (to appear).
2. Gutschwager, C.: On principal hook length partitions and durfee sizes in skew characters. Annals Comb. (to appear).
3. McNamara, P.: Necessary Conditions for Schur-Positivity. J. Algebraic Combin. 28(4), 495-507 (2008).
4. McNamara, P., van Willigenburg, S.: Towards a combinatorial classification of skew Schur functions. Trans. Amer. Math. Soc. (to appear).
5. Reiner, V., Shaw, K.M., van Willigenburg, S.: Coincidences among skew Schur functions. Adv. Math. 216(1), 118-152 (2007).
6. Sagan, B.E.: The Symmetric Group-Representations, Combinatorial Algorithms, and Symmetric Functions, 2nd edn. Springer, New York (2001)
7. Stanley, R.P.: Enumerative Combinatorics, vol.
2. Cambridge University Press, Cambridge (2001)
8. Stembridge, J.R.: SF-package for maple.
2. Gutschwager, C.: On principal hook length partitions and durfee sizes in skew characters. Annals Comb. (to appear).
3. McNamara, P.: Necessary Conditions for Schur-Positivity. J. Algebraic Combin. 28(4), 495-507 (2008).
4. McNamara, P., van Willigenburg, S.: Towards a combinatorial classification of skew Schur functions. Trans. Amer. Math. Soc. (to appear).
5. Reiner, V., Shaw, K.M., van Willigenburg, S.: Coincidences among skew Schur functions. Adv. Math. 216(1), 118-152 (2007).
6. Sagan, B.E.: The Symmetric Group-Representations, Combinatorial Algorithms, and Symmetric Functions, 2nd edn. Springer, New York (2001)
7. Stanley, R.P.: Enumerative Combinatorics, vol.
2. Cambridge University Press, Cambridge (2001)
8. Stembridge, J.R.: SF-package for maple.