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EnglishIn 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.
| Autori: | |
| Titolo: | Irreducible characters of finite simple groups constant at the p-singular elements |
| Digital Object Identifier (DOI): | http://dx.doi.org/10.4171/RSMUP/136-4 |
| Data di pubblicazione: | 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. |
| Lingua: | Inglese |
| Rivista: | |
| Citazione: | 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] |
| Appare nelle tipologie: | Articolo in rivista, Nota a sentenza |
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