Spherical functions and aq-analogue of Kostant's weight multiplicity formula
Spherical functions and aq-analogue of Kostant's weight multiplicity formula
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DOI：
10.1007/bf01389223
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发表时间：
1982-10
影响因子：
3.1
通讯作者：
S. Kato
中科院分区：
文献类型：
--
作者：
S. Kato
本文的目的是给出Lusztig [6]最近提出的复半单李代数不可约表示的Kostant重数公式的一个q-模拟。为了证明这一点，我们广泛地使用了由Satake，Macdonald等人开发的p-adic群（或Hecke代数）上的球函数理论。在证明上述结果的过程中，我们给出了Lusztig [6]中用交同调（或Kazhdan-Lusztig多项式Py，w）描述权重数的定理的一个简短证明。
The purpose of this paper is to give a q-analogue of Kostant's weight multiplicity formula for irreducible representations of complex semisimple Lie algebras, conjectured by Lusztig [6] quite recently. To prove this, we use the theory of spherical functions on p-adic groups (or on Hecke algebras) developed by Satake, Macdonald et al. extensively. In the course of the proof of the above result, we give a short proof of the theorem of Lusztig [6] which describes the weight multiplicities in terms of intersection homology (or Kazhdan-Lusztig polynomials Py, w).