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Representations of Algebraic Groups, Second edition
About this Title
Jens Carsten Jantzen, Aarhus University, Aarhus, Denmark
Publication: Mathematical Surveys and Monographs
Publication Year:
2003; Volume 107
ISBNs: 978-0-8218-4377-2 (print); 978-1-4704-1334-7 (online)
DOI: https://doi.org/10.1090/surv/107
MathSciNet review: MR2015057
MSC: Primary 20G05; Secondary 17B10
ReadershipTable of Contents
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Front/Back Matter
Part I. General theory
- 1. Schemes
- 2. Group schemes and representations
- 3. Induction and injective modules
- 4. Cohomology
- 5. Quotients and associated sheaves
- 6. Factor groups
- 7. Algebras of distributions
- 8. Representations of finite algebraic groups
- 9. Representations of Frobenius kernels
- 10. Reduction mod $p$
Part II. Representations of reductive groups
- 1. Reductive groups
- 2. Simple $G$–modules
- 3. Irreducible representations of the Frobenius kernels
- 4. Kempf’s Vanishing theorem
- 5. The Borel-Bott-Weil theorem and Weyl’s character formula
- 6. The linkage principle
- 7. The translation functors
- 8. Filtrations of Weyl modules
- 9. Representations of $G_rT$ and $G_rB$
- 10. Geometric reductivity and other applications of the Steinberg modules
- 11. Injective $G_r$–modules
- 12. Cohomology of the Frobenius kernels
- 13. Schubert schemes
- 14. Line bundles on Schubert schemes
- A. Truncated categories and Schur algebras
- B. Results over the integers
- C. Lusztig’s conjecture and some consequences
- D. Radical filtrations and Kazhdan-Lusztig polynomials
- E. Tilting modules
- F. Frobenius splitting
- G. Frobenius splitting and good filtrations
- H. Representations of quantum groups