Hook removal operators on the odd Young graph
Algebraic Combinatorics, Volume 2 (2019) no. 2, pp. 249-274.

In this article we consider hook removal operators on odd partitions, i.e., partitions labelling odd-degree irreducible characters of finite symmetric groups. In particular we complete the discussion, started in [8] and developed in [3], concerning the commutativity of such operators.

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DOI: 10.5802/alco.42
Classification: 20C15
Mots-clés : Symmetric groups, Young graph

Bessenrodt, Christine 1; Giannelli, Eugenio 2; Olsson, Jørn B. 3

1 Institute for Algebra, Number Theory and Discrete Mathematics, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany
2 Dipartimento di Matematica “U. Dini”, Université degli Studi di Firenze, Firenze, 50134 Italy
3 Department of Mathematical Sciences, University of Copenhagen, DK-2100 Copenhagen Ø, Denmark
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Bessenrodt, Christine; Giannelli, Eugenio; Olsson, Jørn B. Hook removal operators on the odd Young graph. Algebraic Combinatorics, Volume 2 (2019) no. 2, pp. 249-274. doi : 10.5802/alco.42. https://alco.centre-mersenne.org/articles/10.5802/alco.42/

[1] Ayyer, Arvind; Prasad, Amritanshu; Spallone, Steven Odd partitions in Young’s lattice, Sémin. Lothar. Comb., Volume 75 (2016), Paper no. B75g, 13 pages | MR | Zbl

[2] Bessenrodt, Christine On hooks of Young diagrams, Ann. Comb., Volume 2 (1998) no. 2, pp. 103-110 | DOI | MR | Zbl

[3] Bessenrodt, Christine; Giannelli, Eugenio; Olsson, Jørn B. Restriction of odd degree characters of 𝔖 n , SIGMA, Symmetry Integrability Geom. Methods Appl., Volume 13 (2017), Paper no. 070, 10 pages | DOI | MR | Zbl

[4] Feit, Walter Characters of finite groups, W. A. Benjamin, 1967, viii+186 pages | MR | Zbl

[5] Giannelli, Eugenio Characters of odd degree of symmetric groups, J. Lond. Math. Soc., Volume 96 (2017) no. 1, pp. 1-14 | DOI | MR | Zbl

[6] Giannelli, Eugenio; Kleshchev, Alexander; Navarro, Gabriel; Tiep, Pham Huu Restriction of odd degree characters and natural correspondences, Int. Math. Res. Not. (2017) no. 20, pp. 6089-6118 | DOI | MR | Zbl

[7] Giannelli, Eugenio; Law, Stacey; Martin, Stuart On the p -subgraph of the Young graph (2018) (to appear in Algebr. Represent. Theory) | arXiv | Zbl

[8] Isaacs, I. Martin; Navarro, Gabriel; Olsson, Jørn B.; Tiep, Pham Huu Character restrictions and multiplicities in symmetric groups, J. Algebra, Volume 478 (2017), pp. 271-282 | DOI | MR | Zbl

[9] James, Gordon The representation theory of the symmetric groups, Lecture Notes in Mathematics, 682, Springer, 1978, v+156 pages | MR

[10] James, Gordon; Kerber, Adalbert The representation theory of the symmetric group, Encyclopedia of Mathematics and Its Applications, 16, Addison-Wesley Publishing Co., 1981, xxviii+510 pages (With a foreword by P. M. Cohn, With an introduction by Gilbert de B. Robinson) | MR | Zbl

[11] McKay, John Irreducible representations of odd degree, J. Algebra, Volume 20 (1972), pp. 416-418 | DOI | MR | Zbl

[12] Olsson, Jørn B. Combinatorics and Representations of finite groups, Vorlesungen aus dem Fachbereich Mathematik der Universität Essen, 20, Univ. GH Essen, 1994, 94 pages | Zbl

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