On weight multiplicities of complex simple Lie algebras

The author introduces the notion of a chopped and sliced cone and shows that the weight multiplicities of semisimple complex Lie algebras are governed by this notion. From this he derives a presentation of the weight multiplicity function as a composition of a vector partition function and a linear map. By virtue of this presentation he obtains structural and asymptotic properties of weight multiplicities; for example a proof of G. Heckman's theorem on the Duistermaat-Heckman measure is obtained in this way. The author describes an algorithm for computing general vector partition functions and gives an implementation as a Maple prototype. Using this program he determines and states the weight multiplicity function of the Lie algebra so5(C) completely.

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