Vol. 97, No. 2, 1981

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ISSN: 0030-8730
Orders of finite algebraic groups

K. F. Lai

Vol. 97 (1981), No. 2, 425–435
Abstract

Let be a simply connected simple algebraic group over a finite field Fq of q elements. The order of the group (Fq) of Fq-rational points of is well-known (cf: Steinberg, Carter). The proof makes use of the Bruhat decomposition and the study of polynomials invariant under the action the Weyl group. In this paper we deduce the order of (Fq) from an explicit formula for the integral M(s,Λ) which occurs in Langlands’ theory of Eisenstein series.

Mathematical Subject Classification 2000
Primary: 20G40
Secondary: 10D40
Milestones
Received: 2 May 1979
Published: 1 December 1981
Authors
K. F. Lai