English

Various Representation Dimensions associated with a Finite Group

Representation Theory 2024-06-21 v1

Abstract

To a finite group GG, one can associate several notions of dimensions (or degrees). In this survey, we attempt to bring together some of the notions of dimensions or degrees defined using representations of the group in General Linear Groups and permutation groups. These are embedding degree, minimal faithful irreducible character degree, minimal faithful permutation representation degree, minimal faithful quasi-permutation representation degree and essential dimension. We briefly present the progress in understanding these notions and the related problems.

Keywords

Cite

@article{arxiv.2406.13279,
  title  = {Various Representation Dimensions associated with a Finite Group},
  author = {Anupam Singh and Ayush Udeep},
  journal= {arXiv preprint arXiv:2406.13279},
  year   = {2024}
}
R2 v1 2026-06-28T17:11:38.778Z