Dynkin-Index

In mathematics, the Dynkin index of an irreducible representation R is defined as

Wherein the generating of illustration. The term bears his name in honor of the Russian mathematician Eugene Dynkin.

For a representation of the Lie algebra with the highest weight of the Dynkin index is defined as

Where the Weyl vector

Equal to half the sum of all positive roots is. Is a special case of the largest root, that is, the adjoint representation, the Dynkin index is equal to the dual Coxeter number.