In representation theory of finite groups an important role is played by irreducible characters of -defect 0, for a prime dividing the group order. These are exactly those vanishing at the -singular elements. In this paper we generalize this notion investigating the irreducible characters that are constant at the -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.
Mots clés : Chevalley groups, alternating groups, irreducible characters, principal block
@article{RSMUP_2016__136__35_0,
author = {Pellegrini, Marco and Zalesski, Alexandre},
title = {Irreducible characters of finite simple groups constant at the $p$-singular elements},
journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
pages = {35--50},
publisher = {European Mathematical Society Publishing House},
address = {Zuerich, Switzerland},
volume = {136},
year = {2016},
doi = {10.4171/RSMUP/136-4},
url = {http://www.numdam.org/articles/10.4171/RSMUP/136-4/}
}
TY - JOUR AU - Pellegrini, Marco AU - Zalesski, Alexandre TI - Irreducible characters of finite simple groups constant at the $p$-singular elements JO - Rendiconti del Seminario Matematico della Università di Padova PY - 2016 SP - 35 EP - 50 VL - 136 PB - European Mathematical Society Publishing House PP - Zuerich, Switzerland UR - http://www.numdam.org/articles/10.4171/RSMUP/136-4/ DO - 10.4171/RSMUP/136-4 ID - RSMUP_2016__136__35_0 ER -
%0 Journal Article %A Pellegrini, Marco %A Zalesski, Alexandre %T Irreducible characters of finite simple groups constant at the $p$-singular elements %J Rendiconti del Seminario Matematico della Università di Padova %D 2016 %P 35-50 %V 136 %I European Mathematical Society Publishing House %C Zuerich, Switzerland %U http://www.numdam.org/articles/10.4171/RSMUP/136-4/ %R 10.4171/RSMUP/136-4 %F RSMUP_2016__136__35_0
Pellegrini, Marco; Zalesski, Alexandre. Irreducible characters of finite simple groups constant at the $p$-singular elements. Rendiconti del Seminario Matematico della Università di Padova, Tome 136 (2016), pp. 35-50. doi : 10.4171/RSMUP/136-4. http://www.numdam.org/articles/10.4171/RSMUP/136-4/
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