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
4 - Rationality, the Frobenius Endomorphism, the Lang–Steinberg Theorem
Published online by Cambridge University Press: 14 February 2020
- 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
This chapter defines Frobenius endomorphisms and Frobenius roots and gives the Lang–Steinberg theorem and its consequences using Galois cohomology. Then it studies and classifies finite reductive groups and studies their (B,N)-pairs.
- Type
- Chapter
- Information
- Representations of Finite Groups of Lie Type , pp. 59 - 78Publisher: Cambridge University PressPrint publication year: 2020