Semi-orthogonal decomposition of
conjugation equivariant sheaves
on the loop group and
affine character sheaves
报告专家：Aron Heleodoro（香港大学）
报告时间：2025年4月14日（星期一）下午16:00-17:00
报告地点：国家天元数学西南中心516
报告摘要：Let $G$ be a connected reductive algebraic group over $\mathbb{F}_q$. In the 80s Lusztig developed the theory of character sheaves, some $G$-equivariant perverse sheaves on $G$, from which one can recover all characters of $G(\mathbb{F}_q)$. Since the 2010s, there has been hope that a similar theory could be developed for $p$-adic groups. In this talk, I will explain a first step in this direction.
Given $G$ a $p$-adic group and $LG$ the associated loop group, I will explain how to define a category $D(\frac{LG}{LG})$ of constructible \'etale sheaves on the quotient stack $\frac{LG}{LG}$. Then I will state a semi-orthogonal decomposition of this category coming from a geometric stratification as well as a computation of the categorical trace of the affine Hecke category as a subcategory of $D(\frac{LG}{LG})$. This is joint work with Xuhua He and Xinwen Zhu.
邀请人：张起帆
