REPRESENTATIONS OF LIE ALGEBRAS ARISING FROM POLYTOPES

Authors : Richard M GREEN

Pages : 27-52

View : 12 | Download : 12

Publication Date : 2008-12-01

Article Type : Research Paper

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