Representations of Algebraic Groups (Broché)

The present book, which is a revised edition of the author's book published in 1987nby Academic Press, is intended to give 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, among others, such important basic notions as induction functor, cohomology, quotients, Frobenius kermels, and reduction mod p.
The second part of the book is devoted to the representation theory of reductive algebraic groups. It includes such topies as the description of simple modules, vanishing theorems, the Borel-Bott-Weil theorem and Weyl's character formula, Schubert schemes and line bundles on them. For this revised edition the author added several chapters describing some later developments, among them Schur algebras.
Lusztig's conjecture, and Kazdan-Lusztig polynomials, tilting modules, and representations of quantum groups.