The Order of the Centralizer of a Regular Element
David G. A. Jackson
Research Report 98-9
Date: 8 April 1998
It is well-known that, in the group of rational points of a connected
reductive algebraic group with connected centre, the centralizer of a
rational regular semisimple element is just the number of rational points
in a certain (twisted) rational maximal torus. The purpose of this paper
is to prove a formula expressing the order of the centralizer of a rational
regular (not necessarily semisimple) element in terms of the class function
of the Weyl group which associates to an element w the number of rational
points in a w-twisted rational maximal torus. The formula uses the notion of
truncation of class functions, introduced in the author's PhD thesis.
algebraic groups. Lie algebras. regular elements. truncation.
AMS Subject Classification (1991)
Secondary: 17B45, 20C15, 20F55
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