论文标题
模块化表示和反射子组
Modular representations and reflection subgroups
论文作者
论文摘要
Hecke类别是模块化表示理论中几个基本问题的核心。我们强调“变形哲学”作为一种概念和计算工具的作用，并提出与卢斯蒂格（Lusztig）的“世代哲学”的可能联系。在几何方面，人们可以理解模棱两可的共同体中的定位。最近，Treumann和Leslie-Lonergan添加了史密斯理论，该理论在考虑MOD P系数时提供了有用的工具。在这种情况下，我们与Hazi的一些出色工作联系。利用安倍晋三在Soergel双模型上的工作，我们能够谴责和推广Hazi的一些结果。我们的目的是说服读者，Hazi和Leslie-Lonergan的工作可以被视为某种本地化，以“良好”的反思子组。这些是我在哈佛大学的2019年数学发展发展上的讲座的注释。
The Hecke category is at the heart of several fundamental questions in modular representation theory. We emphasise the role of the "philosophy of deformations" both as a conceptual and computational tool, and suggest possible connections to Lusztig's "philosophy of generations". On the geometric side one can understand deformations in terms of localisation in equivariant cohomology. Recently Treumann and Leslie-Lonergan have added Smith theory, which provides a useful tool when considering mod p coefficients. In this context, we make contact with some remarkable work of Hazi. Using recent work of Abe on Soergel bimodules, we are able to reprove and generalise some of Hazi's results. Our aim is to convince the reader that the work of Hazi and Leslie-Lonergan can usefully be viewed as some kind of localisation to "good" reflection subgroups. These are notes for my lectures at the 2019 Current Developments in Mathematics at Harvard.
