Irreducible Modular Representations of the Reflection Group G(m,1,n)
In an article published in 1980, Farahat and Peel realized the irreducible modular representations of the symmetric group. One year later, Al-Aamily, Morris, and Peel constructed the irreducible modular representations for a Weyl group of type Bn. In both cases, combinatorial methods were used. Almo...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2015/808520 |
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| author | José O. Araujo Tim Bratten Cesar L. Maiarú |
| author_facet | José O. Araujo Tim Bratten Cesar L. Maiarú |
| author_sort | José O. Araujo |
| collection | DOAJ |
| description | In an article published in 1980, Farahat and Peel realized the irreducible modular representations of the symmetric group. One year later, Al-Aamily, Morris, and Peel constructed the irreducible modular representations for a Weyl group of type Bn. In both cases, combinatorial methods were used. Almost twenty years later, using a geometric construction based on the ideas of Macdonald, first Aguado and Araujo and then Araujo, Bigeón, and Gamondi also realized the irreducible modular representations for the Weyl groups of types An and Bn. In this paper, we extend the geometric construction based on the ideas of Macdonald to realize the irreducible modular representations of the complex reflection group of type G(m,1,n). |
| format | Article |
| id | doaj-art-c2c5fc0dcc634f9388c8de078c818a4b |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-c2c5fc0dcc634f9388c8de078c818a4b2025-02-03T01:11:44ZengWileyJournal of Mathematics2314-46292314-47852015-01-01201510.1155/2015/808520808520Irreducible Modular Representations of the Reflection Group G(m,1,n)José O. Araujo0Tim Bratten1Cesar L. Maiarú2Facultad de Ciencias Exactas, Universidad Nacional del Centro de la Provincia de Buenos Aires, B7000GHG Tandil, ArgentinaFacultad de Ciencias Exactas, Universidad Nacional del Centro de la Provincia de Buenos Aires, B7000GHG Tandil, ArgentinaFacultad de Ciencias Exactas, Universidad Nacional del Centro de la Provincia de Buenos Aires, B7000GHG Tandil, ArgentinaIn an article published in 1980, Farahat and Peel realized the irreducible modular representations of the symmetric group. One year later, Al-Aamily, Morris, and Peel constructed the irreducible modular representations for a Weyl group of type Bn. In both cases, combinatorial methods were used. Almost twenty years later, using a geometric construction based on the ideas of Macdonald, first Aguado and Araujo and then Araujo, Bigeón, and Gamondi also realized the irreducible modular representations for the Weyl groups of types An and Bn. In this paper, we extend the geometric construction based on the ideas of Macdonald to realize the irreducible modular representations of the complex reflection group of type G(m,1,n).http://dx.doi.org/10.1155/2015/808520 |
| spellingShingle | José O. Araujo Tim Bratten Cesar L. Maiarú Irreducible Modular Representations of the Reflection Group G(m,1,n) Journal of Mathematics |
| title | Irreducible Modular Representations of the Reflection Group G(m,1,n) |
| title_full | Irreducible Modular Representations of the Reflection Group G(m,1,n) |
| title_fullStr | Irreducible Modular Representations of the Reflection Group G(m,1,n) |
| title_full_unstemmed | Irreducible Modular Representations of the Reflection Group G(m,1,n) |
| title_short | Irreducible Modular Representations of the Reflection Group G(m,1,n) |
| title_sort | irreducible modular representations of the reflection group g m 1 n |
| url | http://dx.doi.org/10.1155/2015/808520 |
| work_keys_str_mv | AT joseoaraujo irreduciblemodularrepresentationsofthereflectiongroupgm1n AT timbratten irreduciblemodularrepresentationsofthereflectiongroupgm1n AT cesarlmaiaru irreduciblemodularrepresentationsofthereflectiongroupgm1n |