Generalized Characters for Glider Representations of Groups
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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.
KeywordsGroups Glider representations Character theory
Mathematics Subject Classification (2010)20C05
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The first author expresses his gratitude to Geoffrey Janssens and Eric Jespers for fruitful discussions on the calculation of the Jacobson radical and the primitive central idempotents of semigroup algebras appearing in the theory of glider representations.
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