These notes provide a concise introduction to the representation theory of reductive algebraic groups in positive characteristic, with an emphasis on Lusztig's character formula and geometric representation theory. They are based on the first author's notes from a lecture series delivered by the second author at the Simons Centre for Geometry and Physics in August 2019. We intend them to complement more detailed treatments.

中文翻译：

---

代数群几何与模表示理论讲座

这些笔记简要介绍了正特征约简代数群的表示理论，重点介绍了 Lusztig 的字符公式和几何表示理论。它们基于第二作者于 2019 年 8 月在西蒙斯几何和物理中心发表的系列讲座中第一作者的笔记。我们打算用它们来补充更详细的处理。