Computational Bounds for Doing Harmonic Analysis on Permutation Modules of Finite Groups
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...
| Main Authors: | , , , , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
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Springer US
2021
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| Online Access: | https://hdl.handle.net/1721.1/133126 |
| _version_ | 1826208901245173760 |
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| author | Hansen, Michael Koyama, Masanori McDermott, Matthew B. A. Orrison, Michael E. Wolff, Sarah |
| author2 | Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory |
| author_facet | Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory Hansen, Michael Koyama, Masanori McDermott, Matthew B. A. Orrison, Michael E. Wolff, Sarah |
| author_sort | Hansen, Michael |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T14:14:06Z |
| format | Article |
| id | mit-1721.1/133126 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T14:14:06Z |
| publishDate | 2021 |
| publisher | Springer US |
| record_format | dspace |
| spelling | mit-1721.1/1331262024-06-06T18:47:47Z Computational Bounds for Doing Harmonic Analysis on Permutation Modules of Finite Groups Hansen, Michael Koyama, Masanori McDermott, Matthew B. A. Orrison, Michael E. Wolff, Sarah Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory 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. 2021-10-26T15:11:13Z 2021-10-26T15:11:13Z 2021-09 2021-08 2021-10-23T03:22:04Z Article http://purl.org/eprint/type/JournalArticle 1531-5851 1069-5869 https://hdl.handle.net/1721.1/133126 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) en https://doi.org/10.1007/s00041-021-09886-3 Journal of Fourier Analysis and Applications 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. The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature application/pdf Springer US Springer US |
| spellingShingle | Hansen, Michael Koyama, Masanori McDermott, Matthew B. A. Orrison, Michael E. Wolff, Sarah Computational Bounds for Doing Harmonic Analysis on Permutation Modules of Finite Groups |
| title | Computational Bounds for Doing Harmonic Analysis on Permutation Modules of Finite Groups |
| title_full | Computational Bounds for Doing Harmonic Analysis on Permutation Modules of Finite Groups |
| title_fullStr | Computational Bounds for Doing Harmonic Analysis on Permutation Modules of Finite Groups |
| title_full_unstemmed | Computational Bounds for Doing Harmonic Analysis on Permutation Modules of Finite Groups |
| title_short | Computational Bounds for Doing Harmonic Analysis on Permutation Modules of Finite Groups |
| title_sort | computational bounds for doing harmonic analysis on permutation modules of finite groups |
| url | https://hdl.handle.net/1721.1/133126 |
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