Understanding E8 Root Systems: A Comprehensive Guide to Prime Roots and Patterns

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The discussion focuses on understanding E8 root systems, emphasizing their complexity and relevance to the user's work. It highlights that E8 consists of 8 basis roots and 120 positive roots, making it a challenging subject to grasp. Suggestions for further reading include a walkthrough on G2 from a series on Lie algebras, which provides foundational insights. The user shares personal examples of their root systems, noting similarities to established patterns. Overall, mastering E8 root systems requires significant time and study.
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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
 
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