| EPSRC Reference: |
GR/S02341/01 |
| Title: |
Schur algebras, symmetric groups and related algebras |
| Principal Investigator: |
Erdmann, Dr K |
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| Department: |
Mathematical Institute |
| Organisation: |
University of Oxford |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
01 November 2002 |
Ends: |
28 February 2003 |
Value (£): |
4,500
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| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
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Let S(n,r) be a Schur algebra, this has canonical idempoterits e(a) where a is a partition of r with at most n parts, let S(a) be the algebra e(a)S(n,r)e(a). Group algebras of symmetric groups occur as a special case. This project will study the representation theory of these algebras S(a) systematically. By using the theory of cellular algebras we will parametrize the simple modules, and determine its homological properties. In particular we will find out when S(a)is quasi-hereditary and when it is self-injective. For suitable choices of $\alpha$ we will determine the composition factors of associated standard modules. We will use the results, together with spectral sequences constructed in earlier work, to relate extensions of modules for Schur algebras, to extensions of modules of S(a), and in particular of symmetric groups. We will also study q-analogues.
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Key Findings |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Potential use in non-academic contexts |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Impacts |
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| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
| Summary |
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| Date Materialised |
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Sectors submitted by the Researcher |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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| Project URL: |
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| Further Information: |
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| Organisation Website: |
http://www.ox.ac.uk |