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
3 - (B,N)-Pairs; Parabolic, Levi, and Reductive Subgroups; Centralisers of Semi-simple Elements
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
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Summary
The theory of (B,N)-pairs is expounded and applied to reductive groups with its consequences on parabolic subgroups, Levi subgroups and centralisers of semi-simple elements.
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- Representations of Finite Groups of Lie Type , pp. 39 - 58Publisher: Cambridge University PressPrint publication year: 2020
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