The Weyl character formula gives the character of a finite-dimensional irreducible representation
of a compact connected Lie group, or equivalently of
a complex semisimple Lie algebra, from its highest
weight. 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 representation.
is the highest weight,
is half the sum of the positive roots, and 
is the Weyl
group, then
