Representations of algebraic groups / Jens Carsten Jantzen.

Format:

Book

Author/Creator:

Jantzen, Jens Carsten, author.

Series:

Mathematical surveys and monographs ; no. 107.

Mathematical surveys and monographs, 0076-5376 ; volume 107

Language:

English

Subjects (All):

Representations of groups.

Linear algebraic groups.

Physical Description:

1 online resource (594 p.)

Edition:

Second edition.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [2003]

Summary:

Gives an introduction to the general theory of representations of algebraic group schemes. This title deals with representation theory of reductive algebraic groups and includes topics such as the description of simple modules, vanishing theorems, Borel-Bott-Weil theorem and Weyl's character formula, and Schubert schemes and lne bundles on them.

Contents:

""Contents""; ""Introduction""; ""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[sub(r)]T and G[sub(r)]B""; ""10. Geometric Reductivity and Other Applications of the Steinberg Modules""; ""11. Injective G[sub(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""; ""References""; ""List of Notations""; ""Index""; ""A""; ""B""; ""C""; ""D""; ""E""; ""F""; ""G""; ""H""; ""I""; ""J""; ""K""; ""L""; ""M""; ""N""; ""O""; ""P""; ""Q""; ""R""; ""S""; ""T""; ""U""; ""W""; ""Y""; ""Z""

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

Description based on print version record.

ISBN:

1-4704-1334-5