On Tilting Modules and Invariants for Algebraic Groups

  • Stephen Donkin
Chapter
Part of the NATO ASI Series book series (ASIC, volume 424)

Abstract

The theme of this article is the calculation and description of generators of polynomial invariants for groups actions by means of trace functions. In this section we give our main applications of this point of view. In the second section we discuss the general framework and also the beautiful theory of conjugacy classes in algebraic groups due to Steinberg, where trace functions play an important role. This serves as as model for our approach in similar situations. In the third section we describe various results on tilting modules and saturated subgroups of algebraic groups. In Section 4 we explain how part of Steinberg’s set-up may be adapted to the action by conjugation of a closed subgroup H of G, in the framework of “group pairs”. The main result here is that the class functions relative to H are trace functions determined by tilting modules. We conclude with some appendices. In the main body of the text. we have omitted all but the simplest proofs. Instead references to the literature are given for proofs where appropriate and to the Appendices (which are of a somewhat technical nature) where no reference is available.

Keywords

Finite Group Conjugacy Class Algebraic Group Parabolic Subgroup Regular Element 
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Copyright information

© Springer Science+Business Media Dordrecht 1994

Authors and Affiliations

  • Stephen Donkin
    • 1
  1. 1.School of Mathematical SciencesQueen Mary and Westfield CollegeLondonEngland

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