关于本原 Milnor 运算作用于 Dickson 不变量的注记

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

Nguyen Sum

备注：: 6 pages

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AI总结：

本文给出奇素数情形下本原 Milnor 运算作用于 $GL_n$ 在多项式代数 $P_n$ 中 Dickson 不变量代数生成元的公式。

摘要：

在本注记中，我们给出一个公式，描述本原 Milnor 运算对一般线性群 $GL_n=GL(n,\mathbb F_p)$ 的不变量代数生成元的作用；这些生成元位于多项式代数 $P_n=\mathbb F_p[x_1,x_2,\ldots,x_n]$ 中，其中 $p$ 为奇素数。

英文摘要：

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.

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