Dynkin index
Encyclopedia
In mathematics
, the Dynkin index
of a representation
of the Lie algebra
g that has a highest weight
is defined as follows
where the Weyl vector
is equal to half of the sum of all the positive roots of g. In the particular case where
is the highest root, meaning that 
is the adjoint representation
,
is equal to the dual Coxeter number.
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, the Dynkin index
of a representation
of the Lie algebraLie algebra
In mathematics, a Lie algebra is an algebraic structure whose main use is in studying geometric objects such as Lie groups and differentiable manifolds. Lie algebras were introduced to study the concept of infinitesimal transformations. The term "Lie algebra" was introduced by Hermann Weyl in the...
g that has a highest weight
is defined as followswhere the Weyl vector
is equal to half of the sum of all the positive roots of g. In the particular case where
is the highest root, meaning that is the adjoint representationAdjoint representation
In mathematics, the adjoint representation of a Lie group G is the natural representation of G on its own Lie algebra...
,
is equal to the dual Coxeter number.