Adjoint groups, regular unipotent elements and discrete series characters

Lehrer, G. I.

doi:10.1090/S0002-9947-1975-0384915-9

Adjoint groups, regular unipotent elements and discrete series characters
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by G. I. Lehrer

Trans. Amer. Math. Soc. 214 (1975), 249-260

DOI: https://doi.org/10.1090/S0002-9947-1975-0384915-9

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Abstract:

It is shown that if G is a finite Chevalley group or twisted type over a field of characteristic p and U is a maximal p-subgroup of G then any nonlinear irreducible character of U vanishes on regular elements. For groups of adjoint type the linear content of the restriction to U of a discrete series character J of G is calculated and it is deduced that J takes the value 0 or ${( - 1)^s}$ on regular elements of U $(s = {\text {rank}}\;G)$.

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