Kostant partition function (original) (raw)

In representation theory, a branch of mathematics, the Kostant partition function, introduced by Bertram Kostant , of a root system is the number of ways one can represent a vector (weight) as a non-negative integer linear combination of the positive roots . Kostant used it to rewrite the Weyl character formula as a formula (the Kostant multiplicity formula) for the multiplicity of a weight of an irreducible representation of a semisimple Lie algebra. An alternative formula, that is more computationally efficient in some cases, is Freudenthal's formula.