Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Birational induction of nilpotent orbit covers in exceptional types

Matthew Westaway

Abstract

Let $G$ be a semisimple simply connected algebraic group over ${\mathbb C}$ of exceptional type. For each $G$-equivariant nilpotent cover of a nilpotent coadjoint $G$-orbit ${\mathbb O}$, we determine the unique birationally rigid induction datum from which it is birationally induced.

Birational induction of nilpotent orbit covers in exceptional types

Abstract

Let be a semisimple simply connected algebraic group over of exceptional type. For each -equivariant nilpotent cover of a nilpotent coadjoint -orbit , we determine the unique birationally rigid induction datum from which it is birationally induced.
Paper Structure (52 sections, 19 theorems, 282 equations)

This paper contains 52 sections, 19 theorems, 282 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Algebraic groups and Levi subgroups
  4. Nilpotent orbits and covers
  5. Lusztig-Spaltenstein induction
  6. Birational induction
  7. Namikawa space and the Namikawa Weyl group
  8. Birationally rigid nilpotent covers
  9. Computing equivariant fundamental groups for Levi subgroups
  10. Equivariant fundamental groups of Levi subgroups of simply connected $E_6$
  11. Equivariant fundamental groups of Levi subgroups of simply connected $E_7$
  12. Case-by-case arguments
  13. pi=1
  14. pi=Z2
  15. D4A1 in E7
  16. ...and 37 more sections

Key Result

Theorem 1.1

Let $G$ be a semisimple simply connected algebraic group over ${\mathbb C}$ of exceptional type and let $\widetilde{{\mathbb O}}\to {\mathbb O}$ be a $G$-equivariant nilpotent orbit cover, where ${\mathbb O}$ is not a rigid nilpotent orbit. Then the (unique) birationally rigid birational induction d

Theorems & Definitions (31)

  • Theorem 1.1
  • Proposition 2.1
  • Proposition 2.2
  • Proposition 2.3
  • Proposition 2.4
  • Proposition 2.5
  • Remark 1
  • Proposition 2.6
  • Proposition 2.7
  • Theorem 2.8
  • ...and 21 more