English

Computational Bounds for Doing Harmonic Analysis on Permutation Modules of Finite Groups

Representation Theory 2019-10-10 v1

Abstract

We develop an approach to finding upper bounds for the number of arithmetic operations necessary for doing harmonic analysis on permutation modules of finite groups. The approach takes advantage of the intrinsic orbital structure of permutation modules, and it uses the multiplicities of irreducible submodules within individual orbital spaces to express the resulting computational bounds. We conclude by showing that these bounds are surprisingly small when dealing with certain permutation modules arising from the action of the symmetric group on tabloids.

Keywords

Cite

@article{arxiv.1910.03722,
  title  = {Computational Bounds for Doing Harmonic Analysis on Permutation Modules of Finite Groups},
  author = {Michael Hansen and Masanori Koyama and Matthew B. A. McDermott and Michael E. Orrison and Sarah Wolff},
  journal= {arXiv preprint arXiv:1910.03722},
  year   = {2019}
}

Comments

19 pages

R2 v1 2026-06-23T11:38:12.061Z