The main goal of the thesis is to define and give some results about unipotent representations of finite groups of Lye type. The first part is concerned with algebraic groups and their structure, focusing on reductive ones. Then we introduce Frobenius morphisms and finite groups of Lie type; we thus treat rationality questions and properties of finite groups of Lie type, with particular attention to the knowledge gainable from the algebraic groups into which they embed. The final part analyzes aspects of the representation theory of finite groups of Lie type: we examine HarishChandra induction and Lusztig one. The latter allows us to define unipotent representations, which are then studied to some extent.
The main goal of the thesis is to define and give some results about unipotent representations of finite groups of Lye type. The first part is concerned with algebraic groups and their structure, focusing on reductive ones. Then we introduce Frobenius morphisms and finite groups of Lie type; we thus treat rationality questions and properties of finite groups of Lie type, with particular attention to the knowledge gainable from the algebraic groups into which they embed. The final part analyzes aspects of the representation theory of finite groups of Lie type: we examine HarishChandra induction and Lusztig one. The latter allows us to define unipotent representations, which are then studied to some extent.
Unipotent Representations of Finite Groups of Lie Type
COLLACCIANI, ELENA
2021/2022
Abstract
The main goal of the thesis is to define and give some results about unipotent representations of finite groups of Lye type. The first part is concerned with algebraic groups and their structure, focusing on reductive ones. Then we introduce Frobenius morphisms and finite groups of Lie type; we thus treat rationality questions and properties of finite groups of Lie type, with particular attention to the knowledge gainable from the algebraic groups into which they embed. The final part analyzes aspects of the representation theory of finite groups of Lie type: we examine HarishChandra induction and Lusztig one. The latter allows us to define unipotent representations, which are then studied to some extent.File  Dimensione  Formato  

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https://hdl.handle.net/20.500.12608/35007