Extensions of modules over Schur algebras, symmetric groups and Hecke algebras
We study the relation between the cohomology of general linear and symmetric groups and their respective quantizations, using Schur algebras and standard homological techniques to build appropriate spectral sequences. As our methods fit inside a much more general context within the theory of finite-...
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
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2004
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| _version_ | 1826293967155625984 |
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| author | Doty, SR Erdmann, K Nakano, D |
| author_facet | Doty, SR Erdmann, K Nakano, D |
| author_sort | Doty, SR |
| collection | OXFORD |
| description | We study the relation between the cohomology of general linear and symmetric groups and their respective quantizations, using Schur algebras and standard homological techniques to build appropriate spectral sequences. As our methods fit inside a much more general context within the theory of finite-dimensional algebras, we develop our results first in that general setting, and then specialize to the above situations. From this we obtain new proofs of several known results in modular representation theory of symmetric groups. Moreover, we reduce certain questions about computing extensions for symmetric groups and Hecke algebras to questions about extensions for general linear groups and their quantizations. |
| first_indexed | 2024-03-07T03:38:22Z |
| format | Journal article |
| id | oxford-uuid:bd0de98f-e4f4-49c7-b9c9-59389bca5a4b |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T03:38:22Z |
| publishDate | 2004 |
| record_format | dspace |
| spelling | oxford-uuid:bd0de98f-e4f4-49c7-b9c9-59389bca5a4b2022-03-27T05:28:52ZExtensions of modules over Schur algebras, symmetric groups and Hecke algebrasJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:bd0de98f-e4f4-49c7-b9c9-59389bca5a4bEnglishSymplectic Elements at Oxford2004Doty, SRErdmann, KNakano, DWe study the relation between the cohomology of general linear and symmetric groups and their respective quantizations, using Schur algebras and standard homological techniques to build appropriate spectral sequences. As our methods fit inside a much more general context within the theory of finite-dimensional algebras, we develop our results first in that general setting, and then specialize to the above situations. From this we obtain new proofs of several known results in modular representation theory of symmetric groups. Moreover, we reduce certain questions about computing extensions for symmetric groups and Hecke algebras to questions about extensions for general linear groups and their quantizations. |
| spellingShingle | Doty, SR Erdmann, K Nakano, D Extensions of modules over Schur algebras, symmetric groups and Hecke algebras |
| title | Extensions of modules over Schur algebras, symmetric groups and Hecke algebras |
| title_full | Extensions of modules over Schur algebras, symmetric groups and Hecke algebras |
| title_fullStr | Extensions of modules over Schur algebras, symmetric groups and Hecke algebras |
| title_full_unstemmed | Extensions of modules over Schur algebras, symmetric groups and Hecke algebras |
| title_short | Extensions of modules over Schur algebras, symmetric groups and Hecke algebras |
| title_sort | extensions of modules over schur algebras symmetric groups and hecke algebras |
| work_keys_str_mv | AT dotysr extensionsofmodulesoverschuralgebrassymmetricgroupsandheckealgebras AT erdmannk extensionsofmodulesoverschuralgebrassymmetricgroupsandheckealgebras AT nakanod extensionsofmodulesoverschuralgebrassymmetricgroupsandheckealgebras |