Clifford theory for glider representations

Abstract

Classical Clifford theory studies the decomposition of simple $G$-modules into simple $H$-modules for some normal subgroup $H◃G$. In this paper we deal with chains of normal subgroups $1◃G_1◃\cdots ◃G_d=G$, which allow to consider fragments and in particular glider representations. These are given by a descending chain of vector spaces over some field $K$ and relate different representations of the groups appearing in the chain. Picking some normal subgroup $H◃G$ one obtains a normal subchain and one can construct an induced fragment structure. Moreover, a notion of irreducibility of fragments is introduced, which completes the list of ingredients to perform a Clifford theory.

15 pages. There was an erratum at the beginning of section 4. This could be omitted without further consequences to the results in the paper. To appear in Algebras and Representation Theory

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• Glider representations of group algebra filtrations of nilpotent groups