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.

Key phrases

algebraic groups. Lie algebras. regular elements. truncation.

AMS Subject Classification (1991)

Primary: 20G40
Secondary: 17B45, 20C15, 20F55


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