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A dimension formula of closed affine Deligne-Lusztig varieties of parahoric level

Arghya Sadhukhan

Abstract

We establish a dimension formula for certain union $X^G(μ,b)_J$ of affine Deligne-Lusztig varieties associated to arbitrary parahoric level structures of split reductive groups, under certain genericity hypotheses.

A dimension formula of closed affine Deligne-Lusztig varieties of parahoric level

Abstract

We establish a dimension formula for certain union of affine Deligne-Lusztig varieties associated to arbitrary parahoric level structures of split reductive groups, under certain genericity hypotheses.

Paper Structure

This paper contains 25 sections, 11 theorems, 36 equations.

Table of Contents

  1. Introduction
  2. Strategy
  3. Preliminaries
  4. Group-theoretic notations
  5. The $\sigma$-conjugacy classes of $\breve G$
  6. Neutrally acceptable elements
  7. Affine Deligne-Lusztig varieties
  8. Quantum Bruhat graphs
  9. Recollections from previous works
  10. Some standard reductions
  11. Virtual dimension formula
  12. Minimizing distance on the quantum Bruhat graph
  13. Explicit constructions for type $A_n, B_n /C_n$
  14. $J$ is of type $A_n$
  15. $J$ is of type $B_n$ or $C_n$
  16. ...and 10 more sections

Key Result

Theorem \oldthetheorem

Suppose that $\mathbf G$ is a split group and let $[b] \in B(\mathbf G,\mu)$. Then in the following cases:

Theorems & Definitions (22)

  • Theorem \oldthetheorem
  • Theorem \oldthetheorem
  • Lemma \oldthetheorem
  • Lemma \oldthetheorem
  • Lemma \oldthetheorem
  • proof
  • Lemma \oldthetheorem
  • Lemma \oldthetheorem
  • proof
  • Proposition \oldthetheorem
  • ...and 12 more