Lectures on Frobenius Splittings and B-Modules

✍ Scribed by Wilberd van der Kallen (auth.)

• Publisher: Springer Berlin Heidelberg
• Year: 1993
• Tongue: English
• Leaves: 112
• Series: Tata Institute of Fundamental Research Lectures on Mathematics and Physics
• Category: Library

✦ Synopsis

The course given by the author at the Tata Institute in 1992 explains the solution by O. Mathieu of some conjectures in the representation theory of arbitrary semisimple algebraic groups. The conjectures concern filtrations of (tensor products of) "standard" representations; while Demazure studied the representations by means of a particular resolutionof singularities of Schubert varieties, the method of Mathieu involves sheafcohomology and "Frobenius splittings" on a Demazure resolution in finite characteristic p. The notes explain all this, but assume some familiarity with algebraic varieties and semisimple algebraic groups (or Liegroups).

✦ Table of Contents

Content:
Front Matter....Pages N1-x
Preliminaries....Pages 1-8
B-Module Theory....Pages 9-21
Polo’s Theorem....Pages 22-32
Donkin’s Conjecture....Pages 33-47
Joseph’s Conjecture....Pages 48-55
Polo’s Conjecture....Pages 56-67
Other Base Rings....Pages 68-74
Back Matter....Pages 75-102