Classification of skew symmetric matrices

Abstract

The group GL(d,l) = Aut(2d) actsonthe Z-module Hom(A2Zd , Z/aZ) by tp —* q>(aAa) (a € AutZd). Associated with each = [ax , ..., ak] if k G md(A), A a commutative principal ideal ring. Let (dk( )), the kth determinantal divisor of )) 0 is the rank of O. It is evident that (dk( 1 , let (sk(Q>)) denote the ideal {m G A\mdk_x( ) g (dk(®)} if (dk( )) ? 0, and zero otherwise. Then (^WX^-iW) = «(•))■ Note that (5,( )) C (sk_x(Q>)) [3]. Received by the editors March 15, 1989 and, in revised form, April 24, 1989. 1980 Mathematics Subject Classification (1985 Revision). Primary 46K10, 46L40, 15A63, 46L80.