From Macdonald polynomials to a charge statistic beyond type A
From Macdonald polynomials to a charge statistic beyond type A
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从麦克唐纳多项式到超越 A 型的电荷统计量
DOI：
10.1016/j.jcta.2011.11.013
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
Cristian Lenart
中科院分区：
文献类型：
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作者：
Cristian Lenart
电荷是一个关于字的复杂统计量，这是由Lascoux和Schützenberger提出的，他们给出了Lusztig的t-模拟的重量多重数和仿射晶体上的能量函数的正组合公式，两者都是A型。由于这些概念是为所有李类型定义的，因此基于电荷的推广来表达它们一直是一个长期存在的问题。我提出了一种方法来解决这个问题，在经典的李型，最近的Ram-Yip公式的麦克唐纳多项式和量子Bruhat顺序相应的Weyl群的基础上。该方法的细节在A型（我们恢复经典电荷）和C型（我们定义一个新的统计量）中进行。
The charge is an intricate statistic on words, due to Lascoux and Schützenberger, which gives positive combinatorial formulas for Lusztigʼs t-analogue of weight multiplicities and the energy function on affine crystals, both of type A. As these concepts are defined for all Lie types, it has been a long-standing problem to express them based on a generalization of charge. I present a method for addressing this problem in classical Lie types, based on the recent Ram–Yip formula for Macdonald polynomials and the quantum Bruhat order on the corresponding Weyl group. The details of the method are carried out in type A (where we recover the classical charge) and type C (where we define a new statistic).