Heights of Spin Characters in Characteristic 2

  • Christine Bessenrodt
  • Jørn B. Olsson
Part of the Progress in Mathematics book series (PM, volume 141)


Based on our earlier description of the distribution into 2-blocks of the spin characters of the covering groups of symmetric groups we compute the heights of such characters in the blocks containing them. We also give a complete set of labels for the spin characters of minimal height in a 2-block. Another related topic treated here is the determination of the minimal power of 2 dividing a spin character degree and the explicit description of the labels of spin characters with this minimal power of 2 in their degree. Also, an upper bound for the heights of spin characters in 2-blocks is derived, and the labels of spin characters attaining this bound are described.

As an application of our results we show that the 2-blocks of the covering groups of symmetric groups provide further evidence for some important representation theoretical conjectures.


Symmetric Group Irreducible Character Defect Group Projective Representation Minimal Height 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    C. Bessenrodt, J. B. Olsson, The 2-blocks of the symmetric groups, Institut für Experimentelle Mathematik, Essen, Preprint No. 17 (1993).Google Scholar
  2. [2]
    M. Cabanes, Local structure of the p-blocks of S n.,Math. Z. 198 (1988), 519–543.MathSciNetMATHCrossRefGoogle Scholar
  3. [3]
    P. N. Hoffman, J. F. Humphreys, Projective Representations of the Symmetric Groups, Clarendon Press, Oxford 1992.MATHGoogle Scholar
  4. [4]
    J. F. Humphreys, Blocks of projective representations of the symmetric group, J. London Math. Soc. 133 (2) (1986), 441–452.MathSciNetCrossRefGoogle Scholar
  5. [5]
    G. James, A. Kerber, The Representation Theory of the Symmetric Group, Addison-Wesley, 1981.Google Scholar
  6. [6]
    I.G. Macdonald, On the degrees of the irreducible representations of symmetric groups, Bull. London Math. Soc. 3 (1971), 189–192.MathSciNetMATHCrossRefGoogle Scholar
  7. [7]
    A.O. Morris, J. B. Olsson, On P-quotients for spin characters, J. Algebra 15 (1988), 51–82.MathSciNetCrossRefGoogle Scholar
  8. [8]
    J. B. Olsson, Frobenius symbols for partitions and degrees of spin characters, Math. Scand. 61 (1987), 223–247.MathSciNetMATHGoogle Scholar
  9. [9]
    J. B. Olsson, Combinatorics and Representations of Finite Groups, Vorlesungen aus dem Fachbereich Mathematik der Universität GH Essen, Heft 20, 1993.Google Scholar
  10. [10]
    G. R. Robinson, Local Structure, Vertices and Alperin’s Conjecture. Preprint 1994Google Scholar
  11. [11]
    I. Schur, Über die Darstellung der symmetrischen und der alternierende Gruppe durch gebrochene lineare Substitutionen, J. reine ang. Math. 39 (1911) 155–250 (ges. Abhandlungen 1, 346–441, Springer-Verlag 1973).CrossRefGoogle Scholar
  12. [12]
    A. Wagner, An observation on the degrees of projective representations of the symmetric and alternating group over an arbitrary field, Arch. Math. 29 (1977), 583–589.MATHCrossRefGoogle Scholar

Copyright information

© Birkhäuser Boston 1997

Authors and Affiliations

  • Christine Bessenrodt
    • 1
  • Jørn B. Olsson
    • 2
  1. 1.Fakultät für MathematikOtto-von-Guericke-Universität MagdeburgMagdeburgGermany
  2. 2.Matematisk InstitutKøbenhavns UniversitetCopenhagen ØDemark

Personalised recommendations