Let G be an adjoint finite group of Lie type. In this paper we classify the irreducible characters of G which appear with multiplicity 1 in any Gelfand–Graev character of G. Except for groups of type 2^A_2m and 2^G_2, this property identifies the Steinberg character of G (modulo linear characters).
Pellegrini, M. A., A Description of the Steinberg Character using Gelfand–Graev Characters, <<RESULTS IN MATHEMATICS>>, 2015; 67 (1-2): 71-85. [doi:10.1007/s00025-014-0394-2] [http://hdl.handle.net/10807/65509]
A Description of the Steinberg Character using Gelfand–Graev Characters
Pellegrini, Marco Antonio
2015
Abstract
Let G be an adjoint finite group of Lie type. In this paper we classify the irreducible characters of G which appear with multiplicity 1 in any Gelfand–Graev character of G. Except for groups of type 2^A_2m and 2^G_2, this property identifies the Steinberg character of G (modulo linear characters).
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