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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Adjoint groups, regular unipotent elements and discrete series characters


Author: G. I. Lehrer
Journal: Trans. Amer. Math. Soc. 214 (1975), 249-260
MSC: Primary 20C15; Secondary 20G40
MathSciNet review: 0384915
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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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1975-0384915-9
PII: S 0002-9947(1975)0384915-9
Article copyright: © Copyright 1975 American Mathematical Society