JournalsrsmupVol. 136pp. 35–50

Irreducible characters of finite simple groups constant at the pp-singular elements

  • Marco A. Pellegrini

    Università Cattolica del Sacro Cuore, Brescia, Italy
  • Alexandre Zalesski

    University of East Anglia, Norwich, UK
Irreducible characters of finite simple groups constant at the $p$-singular elements cover
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Abstract

In representation theory of finite groups an important role is played by irreducible characters of pp-defect 0, for a prime pp dividing the group order. These are exactly those vanishing at the pp-singular elements. In this paper we generalize this notion investigating the irreducible characters that are constant at the pp-singular elements. We determine all such characters of non-zero defect for alternating, symmetric and sporadic simple groups.

We also classify the irreducible characters of quasi-simple groups of Lie type that are constant at the non-identity unipotent elements.In particular, we show that for groups of BN-pair rank greater than 2 the Steinberg and the trivial characters are the only characters in question. Additionally, we determine all irreducible characters whose degrees differ by 1 from the degree of the Steinberg character.

Cite this article

Marco A. Pellegrini, Alexandre Zalesski, Irreducible characters of finite simple groups constant at the pp-singular elements. Rend. Sem. Mat. Univ. Padova 136 (2016), pp. 35–50

DOI 10.4171/RSMUP/136-4