Let G be a finite simple group of Lie type. In this paper, we study characters of G that vanish at the non-semisimple elements and whose degree is equal to the order of a maximal unipotent subgroup of G. Such characters can be viewed as a natural generalization of the Steinberg character. For groups G of small rank we also determine the characters of this degree vanishing only at the non-identity unipotent elements.
Pellegrini, M. A., Zalesski, A., On characters of Chevalley groups vanishing at the non-semisimple elements, <<INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION>>, 2016; 26 (04): 789-841. [doi:10.1142/S0218196716500351] [http://hdl.handle.net/10807/81280]
On characters of Chevalley groups vanishing at the non-semisimple elements
Pellegrini, Marco Antonio
;Zalesski, AlexandreSecondo
2016
Abstract
Let G be a finite simple group of Lie type. In this paper, we study characters of G that vanish at the non-semisimple elements and whose degree is equal to the order of a maximal unipotent subgroup of G. Such characters can be viewed as a natural generalization of the Steinberg character. For groups G of small rank we also determine the characters of this degree vanishing only at the non-identity unipotent elements.
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