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Representations of Algebraic Groups

โœ Scribed by Jens Carsten Jantzen (Eds.)

Publisher
Academic Press, Elsevier
Year
1987
Leaves
437
Series
Pure and Applied Mathematics 131
Category
Library
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โœฆ Table of Contents

Content:
Edited by
Page iii

Copyright page
Page iv

Introduction
Pages vii-xiii

1 Schemes
Pages 3-20

2 Group Schemes and Representations
Pages 21-41

3 Induction and Injective Modules
Pages 43-53

4 Cohomology
Pages 55-71

5 Quotients and Associated Sheaves
Pages 73-94

6 Factor Groups
Pages 95-107

7 Agebras of Distributions
Pages 109-127

8 Representations of Finite Algebraic Groups
Pages 129-144

9 Representations of Frobenius Kernels
Pages 145-160

10 Reduction mod p
Pages 161-170

1 Reductive Groups
Pages 173-195

2 Groups Simple G-Modules
Pages 197-211

3 Irreducible Representations of the Frobenius Kernels
Pages 213-226

4 Kempf's Vanishing Theorem
Pages 227-241

5 The Borel-Bott-Weil Theorem and Weyl's Character Formula
Pages 243-258

6 The Linkage Principle
Pages 259-280

7 The Translation Functors
Pages 281-296

8 Filtrations of Weyl Modules
Pages 297-318

9 Representations of GrT and GrB
Pages 319-336

10 Geometric Reductivity and Other Applications of the Steinberg Modules
Pages 337-349

11 Injective Gr-Modules
Pages 351-368

12 Cohomology of the Frobenius Kernels
Pages 369-379

13 Schubert Schemes
Pages 381-394

14 Line Bundles on Schubert Schemes
Pages 395-415

References
Pages 417-434

Index
Pages 435-438

List of Notations
Pages 439-443

๐Ÿ“œ SIMILAR VOLUMES

Representations of Algebraic Groups
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โœ Jens Carsten Jantzen ๐Ÿ“‚ Library ๐Ÿ“… 1987 ๐Ÿ› Academic Press ๐ŸŒ English

Back in print from the AMS, the first part of this book is an introduction to the general theory of representations of algebraic group schemes. Here, Janzten describes important basic notions: induction functors, cohomology, quotients, Frobenius kernels, and reduction mod $p$, among others. The seco

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Back in print from the AMS, the first part of this book is an introduction to the general theory of representations of algebraic group schemes. Here, Janzten describes important basic notions: induction functors, cohomology, quotients, Frobenius kernels, and reduction mod $p$, among others. The seco

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The book contains several well-written, accessible survey papers in many interrelated areas of current research. These areas cover various aspects of the representation theory of Lie algebras, finite groups of Lie types, Hecke algebras, and Lie superalgebras. Geometric methods have been instrumental