PreprintCC BY 4.0arXiv
Non-Induced Representations in Characteristic Zero
Abstract
This paper explores the failure of induction from all proper subgroups to generate the full representation ring, measured by a quotient group Qk(G). We extend existing results for cyclic groups to all finite abelian groups and calculate this quotient for all finite groups over fields of characteristic 0 by reducing to the abelian case. We briefly discuss extensions to positive characteristics via modular representation theory. Finally, we detail our result for certain well-known families of groups.
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BibTeX
@misc{dimmock2026noninduced,
title = {{Non-Induced Representations in Characteristic Zero}},
author = {Sean Dimmock},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.33086},
eprint = {2610.33086},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.33086},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Non-Induced Representations in Characteristic Zero
AU - Sean Dimmock
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.33086
UR - https://arxiv.org/abs/2610.33086
AB - This paper explores the failure of induction from all proper subgroups to generate the full representation ring, measured by a quotient group Q_k(G). We extend existing results for cyclic groups to all finite abelian groups and calculate this quotient for all finite groups over fields of characteristic 0 by reducing to the abelian case. We briefly discuss extensions to positive characteristics via modular representation theory. Finally, we detail our result for certain well-known families of groups.
ER -