范畴Moy-Prasad理论
Categorical Moy-Prasad theory
摘要：
我们对Moy-Prasad在[MP 94]中提出的理论进行了分类。更准确地说，我们定义了一个深度过滤的任何范畴的循环组$G((t))$的行动，并证明了$2$ -范畴生成语句的启发下，未精炼的最小K-类型的理论。利用我们的生成定理，我们计算的Whittaker层的范畴和范畴的Kac-Moody模的深度过滤。在Whittaker方面，我们证明了它恢复并扩展了Raskin在[Ras 16]中构造的过滤。对于KM模，我们的计算编码了几个新的本地化语句，以及确认Chen-Kamgarpour的猜想。
英文摘要：
We categorify the theory developed by Moy-Prasad in [MP94]. More precisely, we define a depth filtration on any category with an action of the loop group $G((t))$ and prove a $2$-categorical generation statement inspired by the theory of unrefined minimal K-types. Using our generation theorem, we compute the depth filtration on the category of Whittaker sheaves and on the category of Kac-Moody modules. On the Whittaker side, we show that it recovers and extends the filtration constructed by Raskin in [Ras16]. For KM modules, our computation encodes several new localization statements, as well as confirming a conjecture of Chen-Kamgarpour.
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