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Journal of Group Theory

Editor-in-Chief: Parker, Christopher W.

Managing Editor: Wilson, John S. / Khukhro, Evgenii I. / Kramer, Linus

6 Issues per year


IMPACT FACTOR 2017: 0.581

CiteScore 2017: 0.53

SCImago Journal Rank (SJR) 2017: 0.778
Source Normalized Impact per Paper (SNIP) 2017: 0.893

Mathematical Citation Quotient (MCQ) 2017: 0.45

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ISSN
1435-4446
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Volume 17, Issue 6

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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
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/ Mark Wildon
Published Online: 2014-05-06 | DOI: https://doi.org/10.1515/jgth-2014-0023

Abstract

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.

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Citing Articles

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[1]
Mark Wildon
SIAM Journal on Discrete Mathematics, 2016, Volume 30, Number 3, Page 1526
[2]
Rowena Paget and Mark Wildon
Journal of the London Mathematical Society, 2016, Volume 93, Number 2, Page 301

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