Glider representations of group algebra filtrations of nilpotent groups

TL;DR

This paper explores the structure and classification of glider representations in finite groups, especially nilpotent groups, introducing generalized character theory and extending classical Clifford theory.

Contribution

It provides a characterization of irreducible glider representations and extends classical representation theory concepts to the context of group algebra filtrations.

Findings

Characterization of irreducible gliders for p-groups

Introduction of generalized character theory for glider representations

Extension of decomposition groups in Clifford theory

Abstract

We continue the study of glider representations of finite groups $G$ with given structure chain of subgroups $e \subset G_1 \subset \ldots \subset G_d = G$. We give a characterization of irreducible gliders of essential length $e \leq d$ which in the case of $p$-groups allows to prove some results about classical representation theory. The paper also contains an introduction to generalized character theory for glider representations and an extension of the decomposition groups in the Clifford theory. Furthermore, we study irreducible glider representations for finite nilpotent groups.