论文标题
分级谎言代数，傅立叶变换和原始对
Graded Lie algebras, Fourier transform and primitive pairs
论文作者
论文摘要
在本文中，我们研究了分级谎言代数的傅立叶变换。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）$的中央器。在此处，在$ \ bbbk $的现场假设下，还假设对组$ g $的猜想有两个猜想，我们证明了傅立叶变换将平等综合体发送给平等综合体。原始对在Lusztig的论文\ cite {lu}中发挥了重要作用，以证明在分级设置中的块分解。该项目的一个长期目标是证明在积极特征上是类似的块分解。在本文中，我们试图了解原始对及其与傅立叶变换的关系。
In this paper we study the Fourier transform on graded Lie algebras. 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 $χ(\mathbb{C}^\times)$. Here under some assumptions on the field $\Bbbk$ and also assuming two conjectures for the group $G$, we prove that the Fourier transform sends parity complexes to parity complexes. Primitive pairs have played an important role in Lusztig's paper \cite{Lu} to prove a block decomposition in the graded setting. A long term goal of this project is to prove a similar block decomposition in positive characteristic. In this paper we have tried to understand the primitive pair and its relation with the Fourier transform.
