ABSTRACT
In this chapter we study glider theory for algebra filtrations FKG on group algebras KG which arise by considering a chain of subgroups 1 < G 1 < … < G d = G, G a finite group. For the easiest chain 1 < G we give a characterization of the irreducible gliders of essential length 1 and with zero body. We use this to show some results about ordinary representation theory for nilpotent groups. After constructing the induced glider for a normal subchain of subgroups, we perform a Clifford theory, provide some geometric aspects and study relations between the appearing decomposition groups. Restricting to nilpotent groups GH of order p k q l we define the tensor product of an FKG-glider with an FKH-glider, turning it into an FKGH-glider and we discuss when an FKGH-glider representation comes from a tensor product of an FKG- and an FKH-glider.
