A combinatorial construction for simply-laced Lie algebras |
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Institution: | School of Mathematics, UNSW, Sydney, NSW, 2052, Australia |
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Abstract: | 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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