论文标题
在Unity III根部的量化标志歧管上的差分运算符
Differential operators on quantized flag manifolds at roots of unity III
论文作者
论文摘要
我们描述了在量化的统一范围内的扭曲差分运算符的捆捆的捆绑符号的共同体，该量子的根源是统一的命令。从此和我们先前的结果来看，对于de concini-kac类型量化了包络代数，其中参数$ q $专门针对统一的根源，其命令是主要的力量，具有一定的不可减至的中心字符的不可约合模块的数量与相应Springer光纤的总共生组的维度相吻合。这给出了lusztig的猜想的弱版，涉及量化包络代数的非限制表示。
We describe the cohomology of the sheaf of twisted differential operators on the quantized flag manifold at a root of unity whose order is a prime power. It follows from this and our previous results that for the De Concini-Kac type quantized enveloping algebra, where the parameter $q$ is specialized to a root of unity whose order is a prime power, the number of irreducible modules with a certain specified central character coincides with the dimension of the total cohomology group of the corresponding Springer fiber. This gives a weak version of a conjecture of Lusztig concerning non-restricted representations of the quantized enveloping algebra.
