Representations of algebraic groups / Jens Carsten Jantzen.

Format:

Book

Author/Creator:

Jantzen, Jens Carsten.

Series:

Mathematical surveys and monographs ; no. 107.

Mathematical surveys and monographs, 0076-5376 ; v. 107

Language:

English

Subjects (All):

Representations of groups.

Linear algebraic groups.

Physical Description:

xiii, 576 pages : illustrations ; 26 cm.

Edition:

Second edition.

Place of Publication:

Providence, RI : American Mathematical Society, 2003.

Contents:

Part I. General Theory

1. Schemes 3

2. Group Schemes and Representations 19

3. Induction and Injective Modules 37

4. Cohomology 49

5. Quotients and Associated Sheaves 65

6. Factor Groups 85

7. Algebras of Distributions 95

8. Representations of Finite Algebraic Groups 111

9. Representations of Frobenius Kernels 125

10. Reduction mod p 141

Part II. Representations of Reductive Groups

1. Reductive Groups 153

2. Simple G-Modules 175

3. Irreducible Representations of the Frobenius Kernels 189

4. Kempf's Vanishing Theorem 201

5. The Borel-Bott-Weil Theorem and Weyl's Character Formula 217

6. The Linkage Principle 231

7. The Translation Functors 251

8. Filtrations of Weyl Modules 267

9. Representations of G[subscript r]T and G[subscript r]B 291

10. Geometric Reductivity and Other Applications of the Steinberg Modules 315

11. Injective G[subscript r]-Modules 325

12. Cohomology of the Frobenius Kernels 343

13. Schubert Schemes 353

14. Line Bundles on Schubert Schemes 365

A. Truncated Categories and Schur Algebras 385

B. Results over the Integers 411

C. Lusztig's Conjecture and Some Consequences 419

D. Radical Filtrations and Kazhdan-Lusztig Polynomials 439

E. Tilting Modules 457

F. Frobenius Splitting 479

G. Frobenius Splitting and Good Filtrations 501

H. Representations of Quantum Groups 515.

Notes:

Includes bibliographical references (pages 531-568) and index.

ISBN:

0821835270

OCLC:

53091004