Hook removal operators on the odd Young graph
Algebraic Combinatorics, Volume 2 (2019) no. 2, p. 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.
Received : 2017-11-24
Revised : 2018-07-23
Accepted : 2018-08-30
Published online : 2019-03-05
DOI : https://doi.org/10.5802/alco.42
Classification:  20C15
Keywords: Symmetric groups, Young graph
@article{ALCO_2019__2_2_249_0,
     author = {Bessenrodt, Christine and Giannelli, Eugenio and Olsson, J\o rn B.},
     title = {Hook removal operators on the odd Young graph},
     journal = {Algebraic Combinatorics},
     publisher = {MathOA foundation},
     volume = {2},
     number = {2},
     year = {2019},
     pages = {249-274},
     doi = {10.5802/alco.42},
     language = {en},
     url = {https://alco.centre-mersenne.org/item/ALCO_2019__2_2_249_0}
}
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/item/ALCO_2019__2_2_249_0/

[1] Ayyer, Arvind; Prasad, Amritanshu; Spallone, Steven Odd partitions in Young’s lattice, Sémin. Lothar. Comb., Volume 75 (2016), B75g, 13 pages | MR 3510808 | Zbl 1339.05014

[2] Bessenrodt, Christine On hooks of Young diagrams, Ann. Comb., Volume 2 (1998) no. 2, pp. 103-110 | Article | MR 1682922 | Zbl 0929.05081

[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), 070, 10 pages | Article | MR 3692973 | Zbl 1378.20013

[4] Feit, Walter Characters of finite groups, W. A. Benjamin (1967), viii+186 pages | MR 0219636 | Zbl 0166.29002

[5] Giannelli, Eugenio Characters of odd degree of symmetric groups, J. Lond. Math. Soc., Volume 96 (2017) no. 1, pp. 1-14 | Article | MR 3687936 | Zbl 06774739

[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 | Article | MR 3712192

[7] Giannelli, Eugenio; Law, Stacey; Martin, Stuart On the p ' -subgraph of the Young graph (2018) https://arxiv.org/abs/1707.00366 (to appear in Algebr. Represent. Theory)

[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 | Article | MR 3621673 | Zbl 06695602

[9] James, Gordon The representation theory of the symmetric groups, Springer, Lecture Notes in Mathematics, Volume 682 (1978), v+156 pages | MR 513828

[10] James, Gordon; Kerber, Adalbert The representation theory of the symmetric group, Addison-Wesley Publishing Co., Encyclopedia of Mathematics and Its Applications, Volume 16 (1981), xxviii+510 pages (With a foreword by P. M. Cohn, With an introduction by Gilbert de B. Robinson) | MR 644144 | Zbl 0491.20010

[11] Mckay, John Irreducible representations of odd degree, J. Algebra, Volume 20 (1972), pp. 416-418 | Article | MR 0286904 | Zbl 0235.20009

[12] Olsson, Jørn B. Combinatorics and Representations of finite groups, Univ. GH Essen, Vorlesungen aus dem Fachbereich Mathematik der Universität Essen, Volume 20 (1994), 94 pages | Zbl 0796.05095