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.

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.

DOI : 10.4171/RSMUP/136-4
Classification : 20
Mots-clés : Chevalley groups, alternating groups, irreducible characters, principal block
Pellegrini, Marco 1 ; Zalesski, Alexandre 2

1 Università Cattolica del Sacro Cuore, BRESCIA, ITALY
2 University of East Anglia, NORWICH, UNITED KINGDOM
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     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/}
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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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