论文标题
由分级谎言代数产生的奇偶校验滑轮研究
Study of parity sheaves arising from graded Lie algebra
论文作者
论文摘要
令$ g $为一个复杂，连接，还原，代数组和$χ：\ mathbb {c}^\ times \ to g $是固定的cocharacter，它在$ \ mathfrak {g} $上定义分级，$ g $。令$ g_0 $为$χ（\ mathbb {c}^\ times）$的中央器。在本文中，我们在$ \ mathfrak {g} _n $上研究$ g_0 $ equivariant sheaves，在$ \ bbbk $的某些假设和组$ g $的情况下。 $ g $的假设适用于$ gl_n $，对于任何$ g $，它都会恢复特征$ 0 $的lusztig的结果。主要的结果是，每个奇偶校验都作为抛物性对抛物线诱导的直接汇总出现。
Let $G$ be a complex, connected, reductive, algebraic group, and $χ:\mathbb{C}^\times \to G$ be a fixed cocharacter that defines a grading on $\mathfrak{g}$, the Lie algebra of $G$. Let $G_0$ be the centralizer of $χ(\mathbb{C}^\times)$. In this paper, we study $G_0$-equivariant parity sheaves on $\mathfrak{g}_n$, under some assumptions on the field $\Bbbk$ and the group $G$. The assumption on $G$ holds for $GL_n$ and for any $G$, it recovers results of Lusztig in characteristic $0$. The main result is that every parity sheaf occurs as a direct summand of the parabolic induction of some cuspidal pair.
