Computational Bounds for Doing Harmonic Analysis on Permutation Modules of Finite Groups
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41_2021_9886_ReferencePDF.pdf
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Author(s)
Hansen, Michael
Koyama, Masanori
McDermott, Matthew B. A.
Orrison, Michael E.
Wolff, Sarah
Date Issued
September 2021
Journal
Journal of Fourier Analysis and Applications
Publisher
Springer US
Citation
Hansen, M., Koyama, M., McDermott, M.B.A. et al. Computational Bounds for Doing Harmonic Analysis on Permutation Modules of Finite Groups. J Fourier Anal Appl 27, 80 (2021)
Version
Author's final manuscript
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.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1007/s00041-021-09886-3
