代数群の表現（第２版） Representations of Algebraic Groups (Mathematical Surveys and Monographs) （2ND）

Jantzen, Jens Carsten

American Mathematical Society（2004/02発売）

• 製本 Hardcover:ハードカバー版／ページ数 576 p.
• 言語 ENG
• 商品コード 9780821835272
• DDC分類 512.2

基本説明

Originally published in 1987 by Academic Press. For this revised edition the author added nearly 150 pages of new material describing some later developments, among them Schur algebras, Lusztig's conjecture and Kazhdan-Lusztig polynomials, and more.

Full Description

Now back in print by the AMS, this is a significantly revised edition of a book originally published in 1987 by Academic Press. This book gives the reader an introduction to the theory of algebraic representations of reductive algebraic groups. To develop appropriate techniques, the first part of the book is an introduction to the general theory of representations of algebraic group schemes. Here, the author describes important basic notions: induction functors, cohomology, quotients, Frobenius kernels, and reduction mod $p$, among others. The second part of the book is devoted to the representation theory of reductive algebraic groups. It includes topics such as the description of simple modules, vanishing theorems, the Borel-Bott-Weil theorem and Weyl's character formula, and Schubert schemes and line bundles on them. For this revised edition the author added nearly 150 pages of new material describing some later developments, among them Schur algebras, Lusztig's conjecture and Kazhdan-Lusztig polynomials, tilting modules, and representations of quantum groups. He also made major revisions to parts of the old text.
Jantzen's book continues to be the ultimate source of information on representations of algebraic groups in finite characteristics. It is suitable for graduate students and research mathematicians interested in algebraic groups and their representations.

Contents

Group schemes and representations; Induction and injective modules; Cohomology; Quotients and associated sheaves; Factor groups; Algebras of distributions; Representations of finite algebraic groups; Representations of Frobenius kernels; Reduction mod sps; Simple sGs-modules; Irreducible representations of the Frobenius kernels; Kempf's vanishing theorem; The Borel-Bott-Weil theorem and Weyl's character formula; The linkage principle; The translation functors; Filtrations of Weyl modules; Representations of sG rTs and sG rBs; Geometric reductivity and other applications of the Steinberg modules; Injective sG rs-modules; Cohomology of the Frobenius kernels; Schubert schemes; Line bundles on Schubert schemes; Truncated categories and Schur algebras; Results over the integers; Lusztig's conjecture and some consequences; Radical filtrations and Kazhdan-Lusztig polynomials; Tilting modules; Frobenius splitting; Frobenius splitting and good filtrations; Representations of quantum groups; References; List of notations; Index; Group schemes and representations; Induction and injective modules; Cohomology; Quotients and associated sheaves; Factor groups; Algebras of distributions; Representations of finite algebraic groups; Representations of Frobenius kernels; Reduction mod sps; Simple sGs-modules; Irreducible representations of the Frobenius kernels; Kempf's vanishing theorem; The Borel-Bott-Weil theorem and Weyl's character formula; The linkage principle; The translation functors; Filtrations of Weyl modules; Representations of sG rTs and sG rBs; Geometric reductivity and other applications of the Steinberg modules; Injective sG rs-modules; Cohomology of the Frobenius kernels; Schubert schemes; Line bundles on Schubert schemes; Truncated categories and Schur algebras; Results over the integers; Lusztig's conjecture and some consequences; Radical filtrations and Kazhdan-Lusztig polynomials; Tilting modules; Frobenius splitting; Frobenius splitting and good filtrations; Representations of quantum groups; References; List of notations; Index