Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Journal of Group Theory

Editor-in-Chief: Parker, Christopher W.

Managing Editor: Wilson, John S. / Khukhro, Evgenii I. / Burness, T.C.

IMPACT FACTOR 2018: 0.470
5-year IMPACT FACTOR: 0.520

CiteScore 2018: 0.53

SCImago Journal Rank (SJR) 2018: 0.566
Source Normalized Impact per Paper (SNIP) 2018: 1.047

Mathematical Citation Quotient (MCQ) 2018: 0.48

See all formats and pricing
More options …
Volume 17, Issue 6


Character deflations and a generalization of the Murnaghan–Nakayama rule

Anton Evseev / Rowena Paget
  • School of Mathematics, Statistics & Actuarial Science, University of Kent, Canterbury, Kent CT2 7NF, United Kingdom
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Mark Wildon
Published Online: 2014-05-06 | DOI: https://doi.org/10.1515/jgth-2014-0023


Given natural numbers m and n, we define a deflation map from the characters of the symmetric group Smn to the characters of Sn. This map is obtained by first restricting a character of Smn to the wreath product SmSn, and then taking the sum of the irreducible constituents of the restricted character on which the base group Sm × ⋯ × Sm acts trivially. We prove a combinatorial formula which gives the values of the images of the irreducible characters of Smn under this map. We also prove an analogous result for more general deflation maps in which the base group is not required to act trivially. These results generalize the Murnaghan–Nakayama rule and special cases of the Littlewood–Richardson rule. As a corollary we obtain a new combinatorial formula for the character multiplicities that are the subject of the long-standing Foulkes' Conjecture. Using this formula we verify Foulkes' Conjecture in some new cases.

The authors would like to thank Professor Christine Bessenrodt for supplying the reference to Farahat's paper [Proc. Lond. Math. Soc. (3) 4 (1954), 303–316] and an anonymous referee for his or her helpful comments.

About the article

Received: 2013-11-05

Published Online: 2014-05-06

Published in Print: 2014-11-01

Citation Information: Journal of Group Theory, Volume 17, Issue 6, Pages 1035–1070, ISSN (Online) 1435-4446, ISSN (Print) 1433-5883, DOI: https://doi.org/10.1515/jgth-2014-0023.

Export Citation

© 2014 by De Gruyter.Get Permission

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

Nicolas Ressayre
Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, 2019
Rowena Paget and Mark Wildon
Proceedings of the London Mathematical Society, 2018
Mark Wildon
SIAM Journal on Discrete Mathematics, 2016, Volume 30, Number 3, Page 1526
Rowena Paget and Mark Wildon
Journal of the London Mathematical Society, 2016, Volume 93, Number 2, Page 301

Comments (0)

Please log in or register to comment.
Log in