Defining relations for certain integrally parameterized Chevalley groups

William Patterson Wardlaw

Vol. 40 (1972), No. 1, 235–250

DOI: 10.2140/pjm.1972.40.235

Abstract

For each faithful finite dimensional irreducible representation R of a finite dimensional simple Lie algebra L over the complex field, this paper treats the integrally parameterized subgroup G_Z of the Chevalley Group G over the rational field Q. For L of type A_l,D_l, or E_l, Lie algebraic methods are used to extend a result of J. Nielson on SL(S,Z) to obtain a finite set of defining relations for G_Z. Similar relations augmented by defining relations for r_{τ^Y z}∖(B₂) are shown to define G_Z when L is of type B_l,C_l, or F₄. (The relations for G_Z(B₂) are not listed here.)

Mathematical Subject Classification 2000

Primary: 20H20

Milestones

Received: 1 September 1970

Published: 1 January 1972