| EPSRC Reference: |
GR/S86167/01 |
| Title: |
Unipotent classes and simple subgroups of algebraic groups |
| Principal Investigator: |
Liebeck, Professor M |
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| Department: |
Mathematics |
| Organisation: |
Imperial College London |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
08 July 2004 |
Ends: |
07 October 2006 |
Value (£): |
13,506
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| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
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Unipotent elements are fundamental to the theory of algebraic groups and finite groups of Lie type and play an important role in both the structure and representation theory. Some parts of the general theory of unipotent elements are quite beautiful, while other parts are in an unsatisfactory state. For example, basic lists of conjugacy classes and centralizer orders of unipotent elements of groups of exceptional Lie type do exist in the literature, but the results are spread over many papers using a variety of techniques and notations, mostly based on a massive case-by-case analysis and offering little overall conceptual understanding. This is an area that is in need of major revision and development, and it is our goal to carry this out. Using some recent new results and methods introduced largely by the proposed Visiting Fellow, Seitz, we propose to develop a new and unified approach to the analysis of unipotent classes and centralizers in finite and algebraic groups of exceptional Lie type. If successful, one by-product of our work will be c some new general information concerning 'saturation' - that is, the embedding of unipotent elements in canonical connected unipotent subgroups - and also concerning the structure of unipotent element centralizers. We plan to apply this to resolve some key remaining open problems in the analysis of subgroups of finite groups of Lie type.Another, related, objective, is to study the conjugacy classes of non-generic finite simple subgroups of exceptional algebraic groups. The possibilities are known up to isomorphism, but the determination of their conjugacy classes is largely uncharted territory.
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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 |
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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.imperial.ac.uk |