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Hodge-Newton indecomposability and a combinatorial identity

Dong Gyu Lim

Abstract

We present a simple alternative viewpoint on Hodge-Newton indecomposability, illustrating its explanatory value through a uniform proof of a combinatorial identity arising from affine Deligne-Lusztig varieties with finite Coxeter part.

Hodge-Newton indecomposability and a combinatorial identity

Abstract

We present a simple alternative viewpoint on Hodge-Newton indecomposability, illustrating its explanatory value through a uniform proof of a combinatorial identity arising from affine Deligne-Lusztig varieties with finite Coxeter part.
Paper Structure (11 sections, 13 theorems, 24 equations)

This paper contains 11 sections, 13 theorems, 24 equations.

Table of Contents

  1. Introduction
  2. Motivation
  3. Convex Hulls
  4. Notations
  5. $B(G,\mu)_\textnormal{indec}$ as the set of convex hulls
  6. $B(G,\mu)$ and lattice points
  7. Proof of the general formula \ref{['generalform']}
  8. Proof of \ref{['equivsmall']}
  9. Lemmas for \ref{['motiv']}
  10. Notations
  11. Two lemmas

Key Result

Theorem 1.1

Fix natural numbers $i< n$, then

Theorems & Definitions (31)

  • Theorem 1.1: HNY
  • Proposition 1.2
  • proof
  • Remark 1.3
  • Definition 2.1
  • Definition 2.2
  • Definition 2.3: Set of "lattice" points
  • Definition 2.4
  • Definition 2.5
  • Theorem 2.6
  • ...and 21 more