| EPSRC Reference: |
GR/R32116/01 |
| Title: |
Tensor Product Theorems for Algebraic Groups |
| Principal Investigator: |
Liebeck, Professor M |
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| Department: |
Mathematics |
| Organisation: |
Imperial College London |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
04 June 2001 |
Ends: |
03 June 2002 |
Value (£): |
10,772
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| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
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The main objective is to prove a tensor product theorem for reductive subgroups of simple algebraic groups. (Phrased in terms of group homomorphisms, this will generalise the well known Steinberg tensor product theorem from representation theory, hence the name.) The idea is to identify various natural classes of reductive subgroups, and then to prove that an arbitrary reductive subgroup must be embedded in a commuting product of some of these as a twisted diagonal subgroup. Such a result would provide a complete conceptual framework for understanding reductive subgroups. Work on this problem for subgroups of type A1 is nearly complete in the case where the algebraic group is defined in good characteristic. We will therefore focus on subgroups of rank greater than 1, and also on the bad characteristic case.Another objective is to begin a study of the conjugacy classes of non-generic simple finite subgroups of exceptional algebraic groups. If the underlying characteristic is a prime p, these are the simple subgroups which are not of Lie type in characteristic p; and if the characteristic is zero, they are arbitrary simple subgroups. The possibilities for the non-generic subgroups are known up to isomorphism, but the determination of their conjugacy classes is one of the last areas of uncharted territory in the field.
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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 |