Submission: 2009, May 19
We analyze certain subgroups of real and complex forms of the Lie group E8, and deduce that any "Theory of Everything" obtained by embedding the gauge groups of gravity and the Standard Model into a real or complex form of E8 lacks certain representation-theoretic properties required by physical reality. The arguments themselves amount to representation theory of Lie algebras along the lines of Dynkin's classic papers and are written for mathematicians.
2000 Mathematics Subject Classification: 22E47 (Primary); 17B25, 81R05, 83E15 (Secondary)
Keywords and Phrases:
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