Abstract

Representation theory seeks to study and classify representations of groups.
While one can focus on individual groups and their representation theory, a richer structure often emerges when considering families of groups. In this broader perspective, one examines how the representation theory evolves within the family and how representations of different groups relate to each other. Classical examples include the symmetric groups and general linear groups over a given finite field. Zelevinsky showed that these families of groups can be described in a very clean and neat way by using the language of Hopf algebras.

In this talk Ehud will discuss a joint work with Tyrone Crisp and Uri Onn, where they prove that a similar structure appears in much more general families of groups, arising as automorphism groups of finite modules over finite rings. He will then explain some applications to the representation theory of the general linear groups over the integers.