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Some applications of the geometric Satake equivalence to modular representation theory

Simon Riche

Abstract

These notes present an application of the geometric Satake equivalence to the description of characters of indecomposable tilting modules for reductive algebraic groups over fields of positive characteristic, obtained in joint work with G. Williamson.

Some applications of the geometric Satake equivalence to modular representation theory

Abstract

These notes present an application of the geometric Satake equivalence to the description of characters of indecomposable tilting modules for reductive algebraic groups over fields of positive characteristic, obtained in joint work with G. Williamson.
Paper Structure (56 sections, 27 theorems, 151 equations)

This paper contains 56 sections, 27 theorems, 151 equations.

Table of Contents

  1. Geometric Satake equivalence and Representation Theory
  2. Contents
  3. Some notation
  4. Acknowledgements
  5. Technical preliminaries
  6. Ind-schemes
  7. Affine Grassmannians
  8. Definition
  9. Representablity
  10. Beauville--Laszlo gluing
  11. Loop spaces
  12. Uniformization
  13. Attractors and Braden's theorem
  14. Definition
  15. Representability
  16. ...and 41 more sections

Key Result

Theorem 1.11

Theorems & Definitions (68)

  • Remark 1.1
  • Definition 1.2
  • Example 1.3
  • Remark 1.4
  • Remark 1.5
  • Definition 1.6
  • Definition 1.7
  • Definition 1.8
  • Definition 1.9
  • Remark 1.10
  • ...and 58 more