REPRESENTATIONS OF LIE ALGEBRAS ARISING FROM POLYTOPES

Year 2008, Volume: 4 Issue: 4, 27 - 52, 01.12.2008

Richard M. Green

Abstract

We present an extremely elementary construction of the simple Lie algebras over C in all of their minuscule representations, using the vertices of various polytopes. The construction itself requires no complicated combinatorics and essentially no Lie theory other than the definition of a Lie algebra; in fact, the Lie algebras themselves appear as by-products of the construction.

Keywords

Lie algebra, minuscule representation, polytope

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