What is Dynkin index?

In mathematics, the Dynkin index

of a representation with highest weight | λ | {\displaystyle |\lambda |} of a compact simple Lie algebra g {\displaystyle {\mathfrak {g}}} that has a highest weight λ {\displaystyle \lambda } is defined by

evaluated in the representation | λ | {\displaystyle |\lambda |}. Here t a {\displaystyle t_{a}} are the matrices representing the generators, and g a b {\displaystyle g_{ab}} is given by

evaluated in the defining representation.