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Character sheaves for classical graded Lie algebras

Ting Xue

Abstract

In this note we study character sheaves for graded Lie algebras arising from inner automorphisms of special linear groups and Vinberg's type II classical graded Lie algebras.

Character sheaves for classical graded Lie algebras

Abstract

In this note we study character sheaves for graded Lie algebras arising from inner automorphisms of special linear groups and Vinberg's type II classical graded Lie algebras.
Paper Structure (22 sections, 8 theorems, 58 equations)

This paper contains 22 sections, 8 theorems, 58 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Classical graded Lie algebras
  4. Hecke algebras associated to complex reflection groups
  5. Nilpotent orbits and component groups
  6. Young $(k,\pm)$-diagrams
  7. Nilpotent orbits and component groups of centralisers
  8. Number of nilpotent orbits in type II
  9. Distinguished nilpotent orbits
  10. Dual strata
  11. Character sheaves: inner automorphisms of $SL_N$
  12. Central characters
  13. Supports of character sheaves
  14. Nilpotent support character sheaves
  15. Character sheaves
  16. ...and 7 more sections

Key Result

Lemma 3.1

We have

Theorems & Definitions (22)

  • Lemma 3.1
  • proof
  • Remark 3.2
  • Lemma 3.3
  • proof
  • Conjecture 4.1
  • Remark 4.2
  • Lemma 4.3
  • proof
  • Corollary 4.4
  • ...and 12 more