“Inductive Methods in the Representation Theory of Finite Groups of Lie Type: An Introduction via GL(n,q)”
Thursday 8 May 2025 h. 14:30 - Room 2BC30 - Elena Collacciani (Padova, Dip. Mat.)
Abstract
Representation theory of groups is the area of mathematics that studies how abstract groups can act on vector spaces – in other words, how to realize groups as collections of linear transformations. Among the many families of finite groups, those of Lie type form a particularly important class, appearing naturally in the classification of finite simple groups.
In this talk, after a brief overview of classical results on the representation theory of finite groups, I will offer a glimpse into the techniques used to construct and classify irreducible representations of finite groups of Lie type. To convey the core ideas while avoiding heavy technicalities, I will focus on the case of the General Linear group over a finite field. Special emphasis will be placed on the role of inductive methods – a fundamental paradigm in representation theory – which often reduce complex algebraic problems to more manageable combinatorial ones. To help develop intuition, I will also present concrete examples of the main objects involved.
The video of the seminar will appear shortly afterwards in this Mediaspace channel.
