The Weyl character formula gives the formal character of a finite-dimensional irreducible Lie algebra representation of a complex
semisimple Lie algebra from its highest
weight. For a compact connected semisimple Lie group, it also gives the group
character of an irreducible group representation
restricted to a maximal torus. If 
is the highest weight,
is half the sum of the positive roots, and 
is the Weyl
group, then
 |
The denominator is the Weyl denominator, and the quotient expands as a finite sum whose coefficients are the weight multiplicities of the Lie algebra representation.
