Generalized characters for glider representations of groups

2018/01/31 by Frederik Caenepeel, Caenepeel, Frederik, F. Van Oystaeyen +2
Mathematics · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #math.GR

paper · pdf · doi:10.48550/arxiv.1801.10368

21 pages, accepted for publication in Algebras and Representation Theory

openalex publication_date 2018/01/31 · arxiv created 2018/11/30 · arxiv updated 2018/12/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Glider representations can be defined for a finite algebra filtration FKG determined by a chain of subgroups 1 < G₁ < ... < 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.

Related

• Glider Representation Rings with a view on distinguishing groups
• On Generalized Characters Whose Values on Nonidentity Elements are Sums of at Most Two Roots of Unity
• A generalized character associated to element orders
• Representations and characters of finite groups
• Localization and sheaves of glider representations