Character restrictions and multiplicities in symmetric groups. (English) Zbl 1423.20006

Isaacs, I. M.; Navarro, Gabriel; Olsson, Jørn B.; Tiep, Pham Huu

J. Algebra 478, 271-282 (2017).

Summary: We give natural correspondences of odd-degree characters of the symmetric groups and some of their subgroups, which can be described easily by restriction of characters, degrees and multiplicities.

MSC:

20C15	Ordinary representations and characters
20C30	Representations of finite symmetric groups

Keywords:

restriction; multiplicities; symmetric groups; odd degree characters; natural correspondences

References:

[1]	Ayyer, A.; Prasad, A.; Spallone, S., Odd partitions in Young’s lattice, Sémin. Lothar. Comb., 75, (2016), Article B75g · Zbl 1339.05014
[2]	Giannelli, E., Characters of odd degree of symmetric groups · Zbl 1434.20007
[3]	Giannelli, E.; Kleshchev, A.; Navarro, G.; Tiep, Pham Huu, Restriction of odd degree characters and natural correspondences, Int. Math. Res. Not., (2017), in press · Zbl 1404.20006
[4]	James, G. D., The representation theory of the symmetric groups, (1978), Springer-Verlag · Zbl 0393.20009
[5]	James, G.; Kerber, A., The representation theory of the symmetric group, Encyclopedia Math. Appl., vol. 16, (1981), Addison-Wesley Publishing Co. Reading, MA
[6]	Macdonald, I. G., On the degrees of the irreducible representations of symmetric groups, Bull. Lond. Math. Soc., 3, 189-192, (1971) · Zbl 0219.20008
[7]	Olsson, J. B., Mckay numbers and heights of characters, Math. Scand., 38, 25-42, (1976) · Zbl 0327.20005
[8]	Olsson, J. B., Combinatorics and representations of finite groups, vol. 20, (1993), Vorlesungen aus dem Fachbereich Mathematik der Universität GH Essen, Universität Essen