On Some Generalization of B. Kostant’s Partition Function
In this note we shall show some useful properties of the partition function given by B. Kostant  associated to complex semi-simple Lie algebras. Some of these properties are shown to be valid also for some generalized versions of Kostant’s partition function (see Theorem 1 below). As an application of these properties we give (Theorem 4) an explicit formula for the multiplicity of the zero-weight in a given irreducible representation of the simple Lie algebra of type (G2).
KeywordsRoot System Partition Function Irreducible Representation Characteristic Content Zero Weight
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