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Glider Representations of Group Algebra Filtrations of Nilpotent Groups

Authors
  • Caenepeel, Frederik1
  • Oystaeyen, Fred Van1
  • 1 University of Antwerp, Department of Mathematics, Antwerp, Belgium , Antwerp (Belgium)
Type
Published Article
Journal
Algebras and Representation Theory
Publisher
Springer Netherlands
Publication Date
Jul 31, 2017
Volume
21
Issue
3
Pages
529–550
Identifiers
DOI: 10.1007/s10468-017-9725-9
Source
Springer Nature
Keywords
License
Yellow

Abstract

We continue the study of glider representations of finite groups G with given structure chain of subgroups e ⊂ G1 ⊂… ⊂ Gd = G. We give a characterization of irreducible gliders of essential length e ≤ d which in the case of p-groups allows to prove some results about classical representation theory. The paper also contains an introduction to generalized character theory for glider representations and an extension of the decomposition groups in the Clifford theory. Furthermore, we study irreducible glider representations for products of groups and nilpotent groups.

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