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A note on the action of the primitive Milnor operations on the Dickson invariants

Nguyen Sum

Abstract

In this note, we present a formula for the action of the primitive Milnor operations on generators of algebra of invariants of the general linear group $GL_n=GL(n, \mathbb F_p)$ in the polynomial algebra $P_n= \mathbb F_p[x_1,x_2,\ldots,x_n]$ with $p$ an odd prime number.

A note on the action of the primitive Milnor operations on the Dickson invariants

Abstract

In this note, we present a formula for the action of the primitive Milnor operations on generators of algebra of invariants of the general linear group in the polynomial algebra with an odd prime number.

Paper Structure

This paper contains 2 sections, 8 theorems, 23 equations.

Table of Contents

  1. Introduction
  2. Main Result

Key Result

Theorem 2.1

$P_n^{GL_n} = \mathbb F_p[Q_{n,0},Q_{n,1},\ldots,Q_{n,n-1}].$

Theorems & Definitions (11)

  • Theorem 2.1: See Dickson dic
  • Theorem 2.2
  • Proposition 2.3: See Smith-Switzer ssw, Wilkerson wil
  • Proposition 2.4
  • Theorem 2.5
  • proof
  • proof : Proof of Theorem \ref{['dlc']}
  • Corollary 2.6: See su2
  • Corollary 2.7
  • Corollary 2.8
  • ...and 1 more