A type B analog of the Lie representation
We describe a type B analog of the much studied Lie representation of the symmetric group. The nth Lie representation of Sn restricts to the regular representation of Sn−1, and our generalization mimics this property. Specifically, we construct a representation of the type B Weyl group Bn that restr...
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| Format: | Article |
| Language: | English |
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Discrete Mathematics & Theoretical Computer Science
2020-04-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
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| Online Access: | https://dmtcs.episciences.org/6327/pdf |
| _version_ | 1797270201018875904 |
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| author | Andrew Berget |
| author_facet | Andrew Berget |
| author_sort | Andrew Berget |
| collection | DOAJ |
| description | We describe a type B analog of the much studied Lie representation of the symmetric group. The nth Lie representation of Sn restricts to the regular representation of Sn−1, and our generalization mimics this property. Specifically, we construct a representation of the type B Weyl group Bn that restricts to the regular representation of Bn−1. We view both of these representations as coming from the internal zonotopal algebra of the Gale dual of the corresponding reflection arrangements. |
| first_indexed | 2024-04-25T02:00:30Z |
| format | Article |
| id | doaj.art-57a8a78e1d5f427b8369a4caf1af59fa |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T02:00:30Z |
| publishDate | 2020-04-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-57a8a78e1d5f427b8369a4caf1af59fa2024-03-07T14:55:20ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502020-04-01DMTCS Proceedings, 28th...10.46298/dmtcs.63276327A type B analog of the Lie representationAndrew Berget0Department of Mathematics [Bellingham]We describe a type B analog of the much studied Lie representation of the symmetric group. The nth Lie representation of Sn restricts to the regular representation of Sn−1, and our generalization mimics this property. Specifically, we construct a representation of the type B Weyl group Bn that restricts to the regular representation of Bn−1. We view both of these representations as coming from the internal zonotopal algebra of the Gale dual of the corresponding reflection arrangements.https://dmtcs.episciences.org/6327/pdf[math.math-co]mathematics [math]/combinatorics [math.co] |
| spellingShingle | Andrew Berget A type B analog of the Lie representation Discrete Mathematics & Theoretical Computer Science [math.math-co]mathematics [math]/combinatorics [math.co] |
| title | A type B analog of the Lie representation |
| title_full | A type B analog of the Lie representation |
| title_fullStr | A type B analog of the Lie representation |
| title_full_unstemmed | A type B analog of the Lie representation |
| title_short | A type B analog of the Lie representation |
| title_sort | type b analog of the lie representation |
| topic | [math.math-co]mathematics [math]/combinatorics [math.co] |
| url | https://dmtcs.episciences.org/6327/pdf |
| work_keys_str_mv | AT andrewberget atypebanalogofthelierepresentation AT andrewberget typebanalogofthelierepresentation |