一个新的权重数和特征标公式
A new formula for weight multiplicities and characters
摘要：
给出了半单李代数的权重数和特征标的一个新公式。我们的公式将这些权重多重性表示为正有理数的和。事实上，该公式更普遍地适用于Heckman和Opdam的雅可比多项式，这是这些特征的单参数变形。作为结果，我们证明，经过适当的规范化，这些多项式的系数本身是多项式的参数与正整数系数。这推广了我们与F.敲杰克多项式。
英文摘要：
We describe a new formula for weight multiplicities and characters of semisimple Lie algebras. Our formula expresses these weight multiplicities as sums of positive rational numbers. In fact, the formula works more generally for the Jacobi polynomials of Heckman and Opdam, which are a one parameter deformation of these characters. As a consequence we prove that after suitable normalization, the coefficients of these polynomials are themselves polynomials in the parameter with positive integral coefficients. This generalizes our earlier joint work with F. Knop on Jack polynomials.
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