Fundamental domains for the general linear group

Douglas Martin Grenier

Vol. 132 (1988), No. 2, 293–317

DOI: 10.2140/pjm.1988.132.293

Abstract

Historically the most familiar fundamental domain for P_n∕GL_n(Z) has been that of Minkowski. This paper develops a new fundamental domain more suited to applications in number theory. It is shown that these domains can be determined explicitly for given n and this is done for n = 3,4,5,6. A reduction algorithm for an arbitrary element of P_n is also determined.

Mathematical Subject Classification 2000

Primary: 11H55

Secondary: 11F72

Milestones

Received: 10 October 1986

Revised: 18 February 1987

Published: 1 April 1988