Cambridge University Press eBooks· 2020· Book chapter
Representations of Finite Groups of Lie Type
- 455citations
- 2020year
Short summary
This book offers an elementary treatment of the representation theory of finite groups of Lie type, now updated with new chapters on Hecke algebras, Green functions, and Lusztig families.
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Key points
- Provides an elementary treatment of representation theory for finite groups of Lie type.
- Includes new chapters on Hecke algebras, Green functions, and Lusztig families.
- Covers basic theory for linear, unitary, orthogonal, and symplectic groups.
- Emphasizes Curtis–Alvis duality map and Mackey's theorem.
- Discusses Deligne–Lusztig induction and Lusztig's Jordan decomposition theorem.
AI-generated from the title and abstract; the full text is not read.
Abstract
On its original publication, this book provided the first elementary treatment of representation theory of finite groups of Lie type in book form. This second edition features new material to reflect the continuous evolution of the subject, including entirely new chapters on Hecke algebras, Green functions and Lusztig families. The authors cover the basic theory of representations of finite groups of Lie type, such as linear, unitary, orthogonal and symplectic groups. They emphasise the Curtis–Alvis duality map and Mackey's theorem and the results that can be deduced from it, before moving on to a discussion of Deligne–Lusztig induction and Lusztig's Jordan decomposition theorem for characters. The book contains the background information needed to make it a useful resource for beginning graduate students in algebra as well as seasoned researchers. It includes exercises and explicit examples.
The authors' abstract, as published at the source. Cambridge University Press eBooks, 2020 · DOI ↗
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Field: Mathematical Physics
Mathematical PhysicsMathematics