From ndmath Mon Jul 17 13:38:48 1989
Date: Mon, 17 Jul 89 13:38:46 EDT
From: ndmath (Bill Dwyer)
Received: by mssun7.MSI.CORNELL.EDU (4.0/1.1nn-Cornell_Mathematical_Sciences_Institute)
	id AA07195; Mon, 17 Jul 89 13:38:46 EDT
Message-Id: <8907171738.AA07195@mssun7.MSI.CORNELL.EDU>
To: cww
Subject: Matrices
Status: R

  Do you have explicit matrices for the reprexsentation of GL(3,2) over some
algebraic number field?   I can't even find the presentation of GL(3,2)
in my mail records.   There's some cryptic reference somewhere to elements
or order 2, 3 and 7.  What are the relations.  
  I just realized over the weekend that the calculation we need should be easy.
Any faithful 3-dimensional representation of  P(1,2) restricts on the normal
Z2xZ2 to the sum of the three distinct non-trivial one dimensional
representations of this group;  therefore, any such representation has three
distinguished lines.  To conjugate one representation to another, all you have
to do is to bring the lines into alignment  --- in other words, if two
representations are conjugate, it is easy to produce the explicit
conjugation between them.  I was going to give this a shot with
MACSYMA.
                                                                     Bill