LSU Digital Commons LSU Digital Commons Calculations with graded perverse-coherent sheaves Calculations with graded perverse-coherent sheaves
LSU Digital Commons LSU Digital Commons Calculations with graded perverse-coherent sheaves Calculations with graded perverse-coherent sheaves
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LSU Digital Commons LSU Digital Commons 使用分级反相干滑轮的计算 使用分级反相相干滑轮的计算
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通讯作者：
R. Acharya
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作者：
Shruthi Prabhakara;R. Acharya
。本文在特征良好的约化群的幂零锥上进行了几种涉及分次(或Gm等变)逆凝聚层的计算。在本文的第一部分，我们计算了某些规格化(或“典范”)简单对象上的Gm-作用量的权重，这与fi的一个古老的预言相一致。在本文的第二部分中，我们显式地刻画了除2或3以外的每个特征中G=PGL3的所有简单的倒相干层。应用包括显式刻画相应量子群的倾斜模的上同调，以及证明当fi的特征大于3时，PCoh Gm(N)从不允许正分次。
. In this paper, we carry out several computations involving graded (or G m -equivariant) perverse-coherent sheaves on the nilpotent cone of a reductive group in good characteristic. In the first part of the paper, we compute the weight of the G m -action on certain normalized (or “canonical”) simple objects, confirming an old prediction of Ostrik. In the second part of the paper, we explicitly describe all simple perverse coherent sheaves for G = PGL 3 , in every characteristic other than 2 or 3. Applications include an explicit de- scription of the cohomology of tilting modules for the corresponding quantum group, as well as a proof that PCoh G m ( N ) never admits a positive grading when the characteristic of the field is greater than 3.