REPRESENTATIONS OF LIE ALGEBRAS ARISING FROM POLYTOPES

REPRESENTATIONS OF LIE ALGEBRAS ARISING FROM POLYTOPES

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.

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  • Department of Mathematics University of Colorado Campus Box 395 Boulder, CO 80309-0395 USA e-mail: rmg@euclid.colorado.edu