Generalized Characters for Glider Representations of Groups

Abstract

Glider representations can be defined for a finite algebra filtration FKG determined by a chain of subgroups 1 ⊂ G1 ⊂… ⊂ Gd = G. In this paper we develop the generalized character theory for such glider representations. We give the generalization of Artin’s theorem and define a generalized inproduct. For finite abelian groups G with chain 1 ⊂ G, we explicitly calculate the generalized character ring and compute its semisimple quotient. The papers ends with a discussion of the quaternion group as a first non-abelian example.