Clifford Theory for Glider Representations

Classical Clifford theory studies the decomposition of simple G-modules into simple H-modules for some normal subgroup H aS(2) G. In this paper we deal with chains of normal subgroups 1aS(2)G (1)aS(2)center dot center dot center dot aS(2)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 aS(2) 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.