Bessenrodt, Christine; Giannelli, Eugenio; Olsson, Jørn B. Restriction of odd degree characters of \(\mathfrak{S}_n\). (English) Zbl 1378.20013 SIGMA, Symmetry Integrability Geom. Methods Appl. 13, Paper 070, 10 p. (2017). Summary: Let \(n\) and \(k\) be natural numbers such that \(2^k < n\). We study the restriction to \(\mathfrak{S}_{n-2^k}\) of odd-degree irreducible characters of the symmetric group \(\mathfrak{S}_n\). This analysis completes the study begun in [A. Ayyer et al., Sémin. Lothar. Comb. 75, B75g, 13 p. (2016; Zbl 1339.05014)] and recently developed in [I. M. Isaacs et al., J. Algebra 478, 271–282 (2017; Zbl 1423.20006)]. Cited in 3 Documents MSC: 20C30 Representations of finite symmetric groups 05A17 Combinatorial aspects of partitions of integers 20C15 Ordinary representations and characters 05E10 Combinatorial aspects of representation theory Keywords:characters of symmetric groups; hooks in partitions PDF BibTeX XML Cite \textit{C. Bessenrodt} et al., SIGMA, Symmetry Integrability Geom. Methods Appl. 13, Paper 070, 10 p. (2017; Zbl 1378.20013) Full Text: DOI arXiv References: [1] Ayyer, Arvind and Prasad, Amritanshu and Spallone, Steven, Odd partitions in Young’s lattice, S\'eminaire Lotharingien de Combinatoire, 75, Art. B75g, 13 pages, (2015) · Zbl 1339.05014 [2] Giannelli, Eugenio and Kleshchev, Alexander and Navarro, Gabriel and Tiep, Pham Huu, Restriction of odd degree characters and natural correspondences, International Mathematics Research Notices, (None) · Zbl 1404.20006 [3] Isaacs, I. M. and Navarro, Gabriel and Olsson, J\orn B. and Tiep, Pham Huu, Character restrictions and multiplicities in symmetric groups, Journal of Algebra, 478, 271-282, (2017) · Zbl 1423.20006 [4] James, Gordon and Kerber, Adalbert, The representation theory of the symmetric group, Encyclopedia of Mathematics and its Applications, 16, xxviii+510, (1981), Addison-Wesley Publishing Co., Reading, Mass. · Zbl 1159.20012 [5] Macdonald, I. G., On the degrees of the irreducible representations of symmetric groups , The Bulletin of the London Mathematical Society, 3, 189-192, (1971) · Zbl 0219.20008 [6] Olsson, J. B., Combinatorics and representations of finite groups, (None) · 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.