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no. 6
Multiplicity-free skew Schur polynomials
Gao, Shiliang1; Hodges, Reuven1; Orelowitz, Gidon1
1 Dept. of Mathematics, U. Illinois at Urbana-Champaign, Urbana, IL 61801, USA
Algebraic Combinatorics, Volume 4 (2021) no. 6, pp. 1073-1117.

We provide a non-recursive, combinatorial classification of multiplicity-free skew Schur polynomials. These polynomials are GL n , and SL n , characters of the skew Schur modules. Our result extends work of H. Thomas–A. Yong, and C. Gutschwager, in which they classify the multiplicity-free skew Schur functions.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/alco.192
Classification: 05E05, 05E10
Keywords: Skew–Schur polynomial, Littlewood–Richardson tableaux, multiplicity-free.

Gao, Shiliang 1; Hodges, Reuven 1; Orelowitz, Gidon 1

1 Dept. of Mathematics, U. Illinois at Urbana-Champaign, Urbana, IL 61801, USA
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Gao, Shiliang; Hodges, Reuven; Orelowitz, Gidon. Multiplicity-free skew Schur polynomials. Algebraic Combinatorics, Volume 4 (2021) no. 6, pp. 1073-1117. doi : 10.5802/alco.192. https://alco.centre-mersenne.org/articles/10.5802/alco.192/

[1] Avdeev, Roman S.; Petukhov, Alexey V. Spherical actions on flag varieties, Mat. Sb., Volume 205 (2014) no. 9, pp. 3-48 | DOI | MR | Zbl

[2] Azenhas, Olga; Conflitti, Alessandro; Mamede, Ricardo Multiplicity-free skew Schur functions with full interval support, Sém. Lothar. Combin., Volume 75 ([2015-2019]), Paper no. Art. B75j, 35 pages | MR | Zbl

[3] Fink, Alex; Mészáros, Karola; St. Dizier, Avery Zero-one Schubert polynomials, Math. Z., Volume 297 (2021) no. 3-4, pp. 1023-1042 | DOI | MR | Zbl

[4] Fomin, Sergey; Greene, Curtis A Littlewood–Richardson miscellany, European J. Combin., Volume 14 (1993) no. 3, pp. 191-212 | DOI | MR | Zbl

[5] Fulton, William; Harris, Joe Representation theory. A first course, Graduate Texts in Mathematics, 129, Springer-Verlag, New York, 1991, xvi+551 pages | DOI | MR | Zbl

[6] Gutschwager, Christian On multiplicity-free skew characters and the Schubert calculus, Ann. Comb., Volume 14 (2010) no. 3, pp. 339-353 | DOI | MR | Zbl

[7] Hodges, Reuven; Lakshmibai, Venkatramani A classification of spherical Schubert varieties in the Grassmannian (2018) (preprint https://arxiv.org/abs/1809.08003)

[8] Howe, Roger Perspectives on invariant theory: Schur duality, multiplicity-free actions and beyond, The Schur lectures (1992) (Tel Aviv) (Israel Math. Conf. Proc.), Volume 8, Bar-Ilan Univ., Ramat Gan, 1995, pp. 1-182 | MR | Zbl

[9] Littlewood, Dudley E.; Richardson, Archibald R. Group characters and algebra, Philos. Trans. R. Soc. Lond., Ser. A, Contain. Pap. Math. Phys. Character, Volume 233 (1934), pp. 99-141 | DOI | Zbl

[10] Magyar, Peter; Weyman, Jerzy; Zelevinsky, Andrei Multiple flag varieties of finite type, Adv. Math., Volume 141 (1999) no. 1, pp. 97-118 | DOI | MR | Zbl

[11] Perrin, Nicolas On the geometry of spherical varieties, Transform. Groups, Volume 19 (2014) no. 1, pp. 171-223 | DOI | MR | Zbl

[12] Stanley, Richard P. Enumerative combinatorics. Vol. 2, Cambridge Studies in Advanced Mathematics, 62, Cambridge University Press, Cambridge, 2001, xii+581 pages | MR | Zbl

[13] Stembridge, John R. Multiplicity-free products of Schur functions, Ann. Comb., Volume 5 (2001) no. 2, pp. 113-121 | DOI | MR | Zbl

[14] Stembridge, John R. Multiplicity-free products and restrictions of Weyl characters, Represent. Theory, Volume 7 (2003), pp. 404-439 | DOI | MR | Zbl

[15] Thomas, Hugh; Yong, Alexander Multiplicity-free Schubert calculus, Canad. Math. Bull., Volume 53 (2010) no. 1, pp. 171-186 | DOI | MR | Zbl

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