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

Marco Antonio Pellegrini, Alexandre Zalesski

Risultato della ricerca: Contributo in rivistaArticolo in rivistapeer review

2 Citazioni (Scopus)

Abstract

In representation theory of finite groups an important role is played by irreducible characters of p-defect 0, for a prime p dividing the group order. These are exactly those vanishing at the p-singular elements. In this paper we generalize this notion investigating the irreducible characters that are constant at the p-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.
Lingua originaleEnglish
pagine (da-a)35-50
Numero di pagine16
RivistaRENDICONTI DEL SEMINARIO MATEMATICO DELL'UNIVERSITA' DI PADOVA
Volume136
DOI
Stato di pubblicazionePubblicato - 2016

Keywords

  • Chevalley groups
  • alternating groups
  • irreducible characters
  • principal block

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