论文标题
类别中的字符公式$ \ MATHCAL O_P $
Character formulas in Category $\mathcal O_p$
论文作者
论文摘要
令$ \ MATHCAL O_P $表示特征$ p> 0 $版本的普通类别的$ \ Mathcal O $用于半粘合综合体代数。在本文中，我们在$ \ Mathcal O_P $中提供了一些（正式的）字符公式。首先，我们专注于不可约的字符。在这里，我们为如何从有限的许多限制的简单模块的字符以及少量的无限尺寸简单模块的字符中获取所有不可约字符的明确公式。接下来，我们证明了Verma模块的强大链接原理，使我们可以将$ \ Mathcal O_P $将其分为有限的链接类总和。有相应的翻译函数，我们使用它们进一步削减确定所有其他所有其他字符所需的不可减至的字符集。然后，我们证明$ \ Mathcal o $上的扭曲函数将$ \ Mathcal o_p $上的扭曲函子携带到扭曲函数上，作为应用程序，我们证明了具有反替代剂最高权重的Verma模块的jantzen型滤波器的角色总和公式。最后，我们在$ \ Mathcal O_P $中记录了将两种倾斜模块的字符关联的公式。
Let $\mathcal O_p$ denote the characteristic $p>0$ version of the ordinary category $\mathcal O$ for a semisimple complex Lie algebra. In this paper we give some (formal) character formulas in $\mathcal O_p$. First we concentrate on the irreducible characters. Here we give explicit formulas for how to obtain all irreducible characters from the characters of the finitely many restricted simple modules as well as the characters of a small number of infinite dimensional simple modules in $\mathcal O_p$ with specified highest weights. We next prove a strong linkage principle for Verma modules which allow us to split $\mathcal O_p$ into a finite direct sum of linkage classes. There are corresponding translation functors and we use these to further cut down the set of irreducible characters needed for determining all others. Then we show that the twisting functors on $\mathcal O$ carry over to twisting functors on $\mathcal O_p$, and as an application we prove a character sum formula for Jantzen-type filtrations of Verma modules with antidominant highest weights. Finally, we record formulas relating the characters of the two kinds of tilting modules in $\mathcal O_p$.
