E8 root system question

[JeremyEbert]

I'm trying to understand root systems better. They seem to be tied to what I've been working on. Any suggestions on books?

here is an e8 root system

http://upload.wikimedia.org/wikipedia/commons/thumb/f/fe/E8_graph.svg/500px-E8_graph.svg.png

here is some of my root system. the prime roots in mine form essentially the same patterns that are showing up in root systems. Zoom in if needed.

http://2.bp.blogspot.com/_u6-6d4_gs...AAAE8/_hov_b0sno4/s1600/prime-+square+12a.png
also a pdf
https://www.physicsforums.com/attachment.php?attachmentid=31636&d=1296068205

 

[fresh_42]

E8 is quite big to start with 8 basis roots and 120 positive roots.
A walkthrough with a small example (G2) is in this series:
https://www.physicsforums.com/insights/lie-algebras-a-walkthrough-the-basics/It explains how it is done, but to work out E8 will take you quite some time.