A Combinatorial Construction for Simply–laced Lie Algebras

@inproceedings{Wildberger2004ACC,
  title={A Combinatorial Construction for Simply–laced Lie Algebras},
  author={N. J. Wildberger},
  year={2004}
}
This paper shows how to uniformly associate Lie algebras to the simply-laced Dynkin diagrams excluding E8 by constructing explicit combinatorial models of minuscule representations using only graph-theoretic ideas. This involves defining raising and lowering operators in a space of ideals of certain distributive lattices associated to sequences of vertices of the Dynkin diagram. 
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