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.

Pellegrini, M. A., Zalesski, A., Irreducible characters of finite simple groups constant at the p-singular elements, <<RENDICONTI DEL SEMINARIO MATEMATICO DELL'UNIVERSITA' DI PADOVA>>, 2016; 136 (N/A): 35-50. [doi:10.4171/RSMUP/136-4] [http://hdl.handle.net/10807/91100]

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

Pellegrini, Marco Antonio
Primo
;
2016

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.
Inglese
Pellegrini, M. A., Zalesski, A., Irreducible characters of finite simple groups constant at the p-singular elements, <<RENDICONTI DEL SEMINARIO MATEMATICO DELL'UNIVERSITA' DI PADOVA>>, 2016; 136 (N/A): 35-50. [doi:10.4171/RSMUP/136-4] [http://hdl.handle.net/10807/91100]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10807/91100
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