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 Harish-Chandra 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 Harish-Chandra 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 Harish-Chandra induction and Lusztig one. The latter allows us to define unipotent representations, which are then studied to some extent.
2021
Unipotent Representations of Finite Groups of Lie Type
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 Harish-Chandra induction and Lusztig one. The latter allows us to define unipotent representations, which are then studied to some extent.
Representation
Unipotent
Group
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.12608/35007