Alperin weight conjecture and related developments

Abstract

The Alperin weight conjecture is central to the modern representation theory of finite groups, and it is still open, despite many different approaches from different points of view. This paper surveys methods and results relating the Alperin weight conjecture, especially the recent developments in the inductive investigation.

Keywords

• Alperin weight conjecture
• reduction theorem
• blocks
• simple groups
• finite groups of Lie type