Kostant partition function

In representation theory, a branch of mathematics, the Kostant partition function, introduced by Bertram Kostant (1958, 1959), of a root system ${\displaystyle \Delta }$ is the number of ways one can represent a vector (weight) as an integral non-negative sum of the positive roots ${\displaystyle \Delta ^{+}\subset \Delta }$. Kostant used it to rewrite the Weyl character formula for the multiplicity of a weight of an irreducible representation of a semisimple Lie algebra.

The Kostant partition function can also be defined for Kac–Moody algebras and has similar properties.

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