Generalized characters for glider representations of groups
Group Theory
2018-12-03 v3
Abstract
Glider representations can be defined for a finite algebra filtration FKG determined by a chain of subgroups 1 < G_1 < ... < G_d = 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.
Cite
@article{arxiv.1801.10368,
title = {Generalized characters for glider representations of groups},
author = {Frederik Caenepeel and Fred Van Oystaeyen},
journal= {arXiv preprint arXiv:1801.10368},
year = {2018}
}
Comments
21 pages, accepted for publication in Algebras and Representation Theory