Equivalent Blocks of Finite General Linear Groups in Non-describing Characteristic
<p>J. Chuang, R. Kessar, and J. Rickard have proved Broué's Abelian defect group conjecture for many symmetric groups. We adapt the ideas of Kessar and Chuang towards finite general linear groups (represented over non-describing characteristic). We then describe Morita equivalences betwee...
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| Natura: | Journal article |
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Elsevier
2002
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| _version_ | 1826263356827238400 |
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| author | Turner, W |
| author_facet | Turner, W |
| author_sort | Turner, W |
| collection | OXFORD |
| description | <p>J. Chuang, R. Kessar, and J. Rickard have proved Broué's Abelian defect group conjecture for many symmetric groups. We adapt the ideas of Kessar and Chuang towards finite general linear groups (represented over non-describing characteristic). We then describe Morita equivalences between certain <em>p</em>-blocks of <em>GL<sub>n</sub></em>(<em>q</em>) with defect group <em>C<sub>pα</sub> x C<sub>pα</sub></em>, as <em>q</em> varies (see Theorem 2). Here <em>p</em> and <em>q</em> are coprime. This generalizes work of S. Koshitani and M. Hyoue, who proved the same result for principal blocks of <em.gl<sub>n</em.gl<sub></p>(<em>q</em>) when <em.p< em=""> = 3, α = 1, in a different way.</em.p<> |
| first_indexed | 2024-03-06T19:50:28Z |
| format | Journal article |
| id | oxford-uuid:23cc6347-5fa4-47d3-b246-8646812a530b |
| institution | University of Oxford |
| last_indexed | 2024-03-06T19:50:28Z |
| publishDate | 2002 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | oxford-uuid:23cc6347-5fa4-47d3-b246-8646812a530b2022-03-26T11:46:10ZEquivalent Blocks of Finite General Linear Groups in Non-describing CharacteristicJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:23cc6347-5fa4-47d3-b246-8646812a530bSymplectic Elements at OxfordElsevier2002Turner, W<p>J. Chuang, R. Kessar, and J. Rickard have proved Broué's Abelian defect group conjecture for many symmetric groups. We adapt the ideas of Kessar and Chuang towards finite general linear groups (represented over non-describing characteristic). We then describe Morita equivalences between certain <em>p</em>-blocks of <em>GL<sub>n</sub></em>(<em>q</em>) with defect group <em>C<sub>pα</sub> x C<sub>pα</sub></em>, as <em>q</em> varies (see Theorem 2). Here <em>p</em> and <em>q</em> are coprime. This generalizes work of S. Koshitani and M. Hyoue, who proved the same result for principal blocks of <em.gl<sub>n</em.gl<sub></p>(<em>q</em>) when <em.p< em=""> = 3, α = 1, in a different way.</em.p<> |
| spellingShingle | Turner, W Equivalent Blocks of Finite General Linear Groups in Non-describing Characteristic |
| title | Equivalent Blocks of Finite General Linear Groups in Non-describing Characteristic |
| title_full | Equivalent Blocks of Finite General Linear Groups in Non-describing Characteristic |
| title_fullStr | Equivalent Blocks of Finite General Linear Groups in Non-describing Characteristic |
| title_full_unstemmed | Equivalent Blocks of Finite General Linear Groups in Non-describing Characteristic |
| title_short | Equivalent Blocks of Finite General Linear Groups in Non-describing Characteristic |
| title_sort | equivalent blocks of finite general linear groups in non describing characteristic |
| work_keys_str_mv | AT turnerw equivalentblocksoffinitegenerallineargroupsinnondescribingcharacteristic |