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E8 Structure Decoded

Posted by Hemos on from the get-it-down-on-paper dept.

arobic writes "A group of mathematicians from US and Europe succeeded in mapping the E8 structure, an example of a Lie group. These were developed by the well-known mathematician Sophus Lie (pronounce Lee) in the last century and are used for many applications, mainly in theoretical physics. This is an important breakthrough as it could help physicists working on Grand Unified Theories (aka GUTs)."

1 of 127 comments (clear)

  1. Representation Theory by l2718 · · Score: 5, Informative

    Apologies -- this post uses a lot of technical jargon. However, the article is so badly written that I decided to post some remarks. And yes, I am a professional mathematician.

    First, what they mapped was not the "structure" of the Lie group E_8 -- the structure of the group has been known for a long time. What they mapped is what are called the "representations" of the group E_8, which is part of Vogan's program to understand the "unitary dual" (=list of representations) for all (reductive) Lie groups.

    Second, this has no relevance to grand unified theories. Even though a (compact) form of E_8 can be the gauge group of a GUT, the relevant representations are finite-dimensional and have been classified by Weyl decades ago.

    Finally, this is an important result. It is relevant to number theory, and to abstract mathematics in general. The fact that a (finite) computer calculation can help determining an infinite list of representation is very nice.