关于Hecke代数与Z-分次扭转、洗牌及Zuckerman函子
On Hecke algebras and $Z$-graded twisting, Shuffling and Zuckerman functors
AI总结：
本文通过导出扭转函子和导出洗牌函子构造了Iwahori-Hecke代数在Z-分次BGG范畴导出范畴上的范畴作用，并给出分次特征标公式及Zuckerman函子作用的刻画。
摘要：
设$g$为具有Weyl群$W$的复半单李代数。设$H(W)$为与$W$相关联的Iwahori-Hecke代数。对每个$w\in W$，令$T_w$和$C_w$分别为对应的$Z$-分次扭转函子和$Z$-分次洗牌函子。本文通过导出扭转函子给出$H(W)$在$Z$-分次BGG范畴$O_0^Z$的导出范畴$D^b(O_0^Z)$上的范畴作用，并通过导出洗牌函子给出$H(W)$在$D^b(O_0^Z)$上的范畴作用。作为应用，我们对每个单反射$s$得到$T_sL(x)$和$C_sL(x)$的分次特征标公式。我们描述了$Z$-分次扭转函子和洗牌函子在对偶Verma模和单模上的作用中出现的分次平移。我们还刻画了导出$Z$-分次Zuckerman函子在单模上的作用。
英文摘要：
Let $g$ be a complex semisimple Lie algebra with Weyl group $W$. Let $H(W)$ be the Iwahori-Hecke algebra associated to $W$. For each $w\in W$, let $T_w$ and $C_w$ be the corresponding $Z$-graded twisting functor and $Z$-graded shuffling functor respectively. In this paper we present a categorical action of $H(W)$ on the derived category $D^b(O_0^Z)$ of the $Z$-graded BGG category $O_0^Z$ via derived twisting functors as well as a categorical action of $H(W)$ on $D^b(O_0^Z)$ via derived shuffling functors. As applications, we get graded character formulae for $T_sL(x)$ and $C_sL(x)$ for each simple reflection $s$. We describe the graded shifts occurring in the action of the $Z$-graded twisting and shuffling functors on dual Verma modules and simple modules. We also characterize the action of the derived $Z$-graded Zuckerman functors on simple modules.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
