zbMATH — the first resource for mathematics

Hook removal operators on the odd Young graph. (English) Zbl 07049525
Summary: 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.
20C15 Ordinary representations and characters
Full Text: DOI arXiv
[1] Ayyer, Arvind; Prasad, Amritanshu; Spallone, Steven, Odd partitions in Young’s lattice, Sémin. Lothar. Comb., 75, 13 p. pp., (2016) · Zbl 1339.05014
[2] Bessenrodt, Christine, On hooks of Young diagrams, Ann. Comb., 2, 2, 103-110, (1998) · Zbl 0929.05081
[3] Bessenrodt, Christine; Giannelli, Eugenio; Olsson, Jørn B., Restriction of odd degree characters of \(\mathfrak{S}_n\), SIGMA, Symmetry Integrability Geom. Methods Appl., 13, 10 p. pp., (2017) · Zbl 1378.20013
[4] Feit, Walter, Characters of finite groups, viii+186 p. pp., (1967), W. A. Benjamin · Zbl 0166.29002
[5] Giannelli, Eugenio, Characters of odd degree of symmetric groups, J. Lond. Math. Soc., 96, 1, 1-14, (2017) · Zbl 1434.20007
[6] Giannelli, Eugenio; Kleshchev, Alexander; Navarro, Gabriel; Tiep, Pham Huu, Restriction of odd degree characters and natural correspondences, Int. Math. Res. Not., 20, 6089-6118, (2017) · Zbl 1404.20006
[7] Giannelli, Eugenio; Law, Stacey; Martin, Stuart, On the \(p^{\prime }\)-subgraph of the Young graph, (2018) · Zbl 1402.20023
[8] Isaacs, I. Martin; Navarro, Gabriel; Olsson, Jørn B.; Tiep, Pham Huu, Character restrictions and multiplicities in symmetric groups, J. Algebra, 478, 271-282, (2017) · Zbl 1423.20006
[9] James, Gordon, The representation theory of the symmetric groups, 682, v+156 p. pp., (1978), Springer
[10] James, Gordon; Kerber, Adalbert, The representation theory of the symmetric group, 16, xxviii+510 p. pp., (1981), Addison-Wesley Publishing Co. · Zbl 0491.20010
[11] McKay, John, Irreducible representations of odd degree, J. Algebra, 20, 416-418, (1972) · Zbl 0235.20009
[12] Olsson, Jørn B., Combinatorics and Representations of finite groups, 20, 94 p. pp., (1994), Univ. GH Essen · Zbl 0796.05095
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.