On signed Young permutation modules and signed p-Kostka numbers
We prove the existence and main properties of signed Young modules for the symmetric group, using only basic facts about symmetric group representations and the Broué correspondence. We then prove new reduction theorems for the signed p-Kostka numbers, defined to be the multiplicities of signed Youn...
| Main Authors: | , , , |
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| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
2018
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| Online Access: | https://hdl.handle.net/10356/88467 http://hdl.handle.net/10220/45793 |
| _version_ | 1811688324375511040 |
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| author | Giannelli, Eugenio Lim, Kay Jin O’Donovan, William Wildon, Mark |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Giannelli, Eugenio Lim, Kay Jin O’Donovan, William Wildon, Mark |
| author_sort | Giannelli, Eugenio |
| collection | NTU |
| description | We prove the existence and main properties of signed Young modules for the symmetric group, using only basic facts about symmetric group representations and the Broué correspondence. We then prove new reduction theorems for the signed p-Kostka numbers, defined to be the multiplicities of signed Young modules as direct summands of signed Young permutation modules. We end by classifying the indecomposable signed Young permutation modules and determining their endomorphism algebras. |
| first_indexed | 2024-10-01T05:30:24Z |
| format | Journal Article |
| id | ntu-10356/88467 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T05:30:24Z |
| publishDate | 2018 |
| record_format | dspace |
| spelling | ntu-10356/884672023-02-28T19:35:28Z On signed Young permutation modules and signed p-Kostka numbers Giannelli, Eugenio Lim, Kay Jin O’Donovan, William Wildon, Mark School of Physical and Mathematical Sciences Permutation Young Modules DRNTU::Science::Mathematics We prove the existence and main properties of signed Young modules for the symmetric group, using only basic facts about symmetric group representations and the Broué correspondence. We then prove new reduction theorems for the signed p-Kostka numbers, defined to be the multiplicities of signed Young modules as direct summands of signed Young permutation modules. We end by classifying the indecomposable signed Young permutation modules and determining their endomorphism algebras. Published version 2018-09-03T04:33:45Z 2019-12-06T17:03:55Z 2018-09-03T04:33:45Z 2019-12-06T17:03:55Z 2017 Journal Article Giannelli, E., Lim, K. J., O’Donovan, W., & Wildon, M. (2017). On signed Young permutation modules and signed p-Kostka numbers. Journal of Group Theory, 20(4), 637–679. doi:10.1515/jgth-2017-0007 1433-5883 https://hdl.handle.net/10356/88467 http://hdl.handle.net/10220/45793 10.1515/jgth-2017-0007 en Journal of Group Theory © 2017 Walter de Gruyter GmbH. This paper was published in Journal of Group Theory and is made available as an electronic reprint (preprint) with permission of Walter de Gruyter GmbH. The published version is available at: [http://dx.doi.org/10.1515/jgth-2017-0007]. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper is prohibited and is subject to penalties under law. 43 p. application/pdf |
| spellingShingle | Permutation Young Modules DRNTU::Science::Mathematics Giannelli, Eugenio Lim, Kay Jin O’Donovan, William Wildon, Mark On signed Young permutation modules and signed p-Kostka numbers |
| title | On signed Young permutation modules and signed p-Kostka numbers |
| title_full | On signed Young permutation modules and signed p-Kostka numbers |
| title_fullStr | On signed Young permutation modules and signed p-Kostka numbers |
| title_full_unstemmed | On signed Young permutation modules and signed p-Kostka numbers |
| title_short | On signed Young permutation modules and signed p-Kostka numbers |
| title_sort | on signed young permutation modules and signed p kostka numbers |
| topic | Permutation Young Modules DRNTU::Science::Mathematics |
| url | https://hdl.handle.net/10356/88467 http://hdl.handle.net/10220/45793 |
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