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Summary

We explain how the decomposition of unipotent Deligne–Lusztig characters is governed by the component groups of special unipotent classes. For each such class a Lusztig Fourier transform matrix is built from the Drinfeld double of the Lusztig quotient of the group of components.

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.

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14 - The Decomposition of Deligne–Lusztig Characters

Summary

Representations of Finite Groups of Lie Type

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2 results

14 - The Decomposition of Deligne–Lusztig Characters

Summary

Representations of Finite Groups of Lie Type