In representation theory, a branch of mathematics, the Kostant partition function, introduced by Bertram Kostant (1958, 1959), of a root system
The Kostant partition function can also be defined for Kac–Moody algebras and has similar properties.
Relation to the Weyl character formula
The values of Kostant's partition function are given by the coefficients of the power series expansion of
where the product is over all positive roots, the sum is over elements
shows that the Weyl character formula
can also be written as
This allows the multiplicities of finite-dimensional irreducible representations in Weyl's character formula to be written as a finite sum involving values of the Kostant partition function, as these are the coefficients of the power series expansion of the denominator of the right hand side.