On the rank varieties and Jordan types of a class of simple modules
Fix a finite group G and an algebraically closed field F of characteristic p. For an FG-module M, the complexity of M is the rate of growth of a minimal projective resolution of M which is a cohomological invariant of M. The rank varieties introduced by Carlson are defined for modules for elementary...
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| Format: | Thesis-Doctor of Philosophy |
| Language: | English |
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Nanyang Technological University
2024
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| Online Access: | https://hdl.handle.net/10356/173694 |
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| Institution: | Nanyang Technological University |
| Language: | English |
| Summary: | Fix a finite group G and an algebraically closed field F of characteristic p. For an FG-module M, the complexity of M is the rate of growth of a minimal projective resolution of M which is a cohomological invariant of M. The rank varieties introduced by Carlson are defined for modules for elementary abelian p-groups and can be extended to modules for G by looking at the restriction to elementary abelian subgroups of G. Moreover, the dimension of the rank variety gives the complexity of the module. In this thesis, I discuss some basic properties of rank varieties and complexities and then review some known results on the complexities of some simple modules for symmetric groups and finite general linear groups. |
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