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A higher-dimensional Chevalley restriction theorem for classical groups in characteristic p

Xiaopeng Xia

Abstract

We establish a theorem concerning the commuting scheme in characteristic p. As a significant application of this theorem, we derive an explicit lower bound for the characteristic p, ensuring the validity of the higher-dimensional Chevalley restriction theorem for classical groups.

A higher-dimensional Chevalley restriction theorem for classical groups in characteristic p

Abstract

We establish a theorem concerning the commuting scheme in characteristic p. As a significant application of this theorem, we derive an explicit lower bound for the characteristic p, ensuring the validity of the higher-dimensional Chevalley restriction theorem for classical groups.
Paper Structure (6 sections, 10 theorems, 40 equations)

This paper contains 6 sections, 10 theorems, 40 equations.

Table of Contents

  1. Introduction
  2. Notations and preliminaries
  3. Castelnuovo–Mumford regularity
  4. Good filtrations and reductive group actions
  5. Schur functor and The Decomposition of the Exterior Algebra
  6. Main theorems

Key Result

Theorem 1.2

Suppose $n\geq 2$, $d\geq 1$, and $G$ is one of groups $GL_n(\mathbb{K})$, $O_n(\mathbb{K})$, $SO_n(\mathbb{K})$ or $Sp_n(\mathbb{K})$.

Theorems & Definitions (26)

  • Conjecture 1.1: Chen-Ngô
  • Theorem 1.2
  • Lemma 2.1
  • proof
  • Definition 2.2
  • Remark 2.3
  • Proposition 2.4
  • proof
  • Proposition 2.5
  • proof
  • ...and 16 more