Book contents
- Frontmatter
- Contents
- Introduction to the Second Edition
- From the Introduction to the First Edition
- 1 Basic Results on Algebraic Groups
- 2 Structure Theorems for Reductive Groups
- 3 (B,N)-Pairs; Parabolic, Levi, and Reductive Subgroups; Centralisers of Semi-simple Elements
- 4 Rationality, the Frobenius Endomorphism, the Lang–Steinberg Theorem
- 5 Harish-Chandra Theory
- 6 Iwahori–Hecke Algebras
- 7 The Duality Functor and the Steinberg Character
- 8 ℓ-Adic Cohomology
- 9 Deligne–Lusztig Induction: The Mackey Formula
- 10 The Character Formula and Other Results on Deligne–Lusztig Induction
- 11 Geometric Conjugacy and the Lusztig Series
- 12 Regular Elements; Gelfand–Graev Representations; Regular and Semi-Simple Characters
- 13 Green Functions
- 14 The Decomposition of Deligne–Lusztig Characters
- References
- Index
13 - Green Functions
Published online by Cambridge University Press: 14 February 2020
Book contents
- Frontmatter
- Contents
- Introduction to the Second Edition
- From the Introduction to the First Edition
- 1 Basic Results on Algebraic Groups
- 2 Structure Theorems for Reductive Groups
- 3 (B,N)-Pairs; Parabolic, Levi, and Reductive Subgroups; Centralisers of Semi-simple Elements
- 4 Rationality, the Frobenius Endomorphism, the Lang–Steinberg Theorem
- 5 Harish-Chandra Theory
- 6 Iwahori–Hecke Algebras
- 7 The Duality Functor and the Steinberg Character
- 8 ℓ-Adic Cohomology
- 9 Deligne–Lusztig Induction: The Mackey Formula
- 10 The Character Formula and Other Results on Deligne–Lusztig Induction
- 11 Geometric Conjugacy and the Lusztig Series
- 12 Regular Elements; Gelfand–Graev Representations; Regular and Semi-Simple Characters
- 13 Green Functions
- 14 The Decomposition of Deligne–Lusztig Characters
- References
- Index
Summary
We review invariants of reflection groups and reflection cosets up to giving a formula for the order of a finite reductive group. We then review the Springer correspondence between local systems on unipotent classes and characters of the Weyl group, and use it to describe the Lusztig–Shoji algorithm to compute Green functions.
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- Information
- Representations of Finite Groups of Lie Type , pp. 225 - 241Publisher: Cambridge University PressPrint publication year: 2020