Basic Sets for the Double Covering Groups of the Symmetric and Alternating Groups in Odd Characteristic

  • Olivier BrunatEmail author
  • Jean-Baptiste Gramain


In this paper, following the methods of Brunat and Gramain (J. Reine Angew. Math. 641, 177–202, 2010), we show that the double covering groups of the symmetric and alternating groups have p-basic sets for any odd prime p.


Basic set Perfect isometries Double covering groups of the symmetric and alternating groups Modular representation theory 

Mathematics Subject Classification (2010)

Primary 20C30, 20C15 Secondary 20C20 


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Part of this work was done at the CIRM in Luminy during a research in pairs stay. The authors wish to thank the CIRM gratefully for their financial and logistical support. The first author is supported by Agence Nationale de la Recherche Projet ACORT ANR-12-JS01-0003. The second author also acknowledges financial support from the Engineering and Physical Sciences Research Council grant Combinatorial Representation Theory EP/M019292/1. The authors wish to thank the referee for several helpful suggestions.


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© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Institut de Mathématiques de Jussieu – Paris Rive Gauche, UFR de MathématiquesUniversité Paris-Diderot Paris 7Paris Cedex 13France
  2. 2.Institute of MathematicsUniversity of AberdeenAberdeenUK

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