Duality for representations of a reductive group over a finite field

Alvis, 1979, The duality operation in the character ring of a finite Chevalley group, Bull. Amer. Math. Soc., 1, 907, 10.1090/S0273-0979-1979-14690-1 Curtis, 1980, Truncation and duality in the character ring of a finite group of Lie type, J. Algebra, 62, 320, 10.1016/0021-8693(80)90185-4 Howlett, 1980, Indiced cuspidal representations and generalized Hecke rings, Invent. Math., 58, 37, 10.1007/BF01402273 N. Kawanaka, Fourier transforms of nilpotently supported invariant functions on a simple Lie algebra over a finite field, preprint, Osaka University.