Canonical p-dimensions of algebraic groups and degrees of basic polynomial invariants

TL;DR

This paper introduces a new uniform method to compute the canonical p-dimension of split algebraic groups using degrees of basic polynomial invariants, with explicit calculations for all split exceptional groups.

Contribution

It provides a novel approach to determine the canonical p-dimension of algebraic groups via polynomial invariants, extending to all split exceptional groups.

Findings

Computed canonical p-dimensions for all split exceptional algebraic groups

Established a uniform method based on polynomial invariants for p-dimension calculation

Enhanced understanding of algebraic group invariants and their degrees

Abstract

In the present notes we provide a new uniform way to compute a canonical p-dimension of a split algebraic group G for a torsion prime p using degrees of basic polynomial invariants described by V.Kac. As an application, we compute the canonical p-dimensions for all split exceptional algebraic groups.