Pseudo-reflection groups and essential dimension

TL;DR

This paper provides a simple formula for the essential dimension of finite pseudo-reflection groups at a prime p, determines the absolute essential dimension for most irreducible cases, and explores an intermediate notion called 'poor man's essential dimension' for finite groups.

Contribution

It introduces a straightforward formula for essential dimension at a prime p and analyzes the 'poor man's' variant, advancing understanding of group invariants.

Findings

Derived a simple formula for essential dimension of pseudo-reflection groups.

Determined absolute essential dimension for most irreducible pseudo-reflection groups.

Explored the concept of 'poor man's essential dimension' for finite groups.

Abstract

We give a simple formula for the essential dimension of a finite pseudo-reflection group at a prime p and determine the absolute essential dimension for most irreducible pseudo-reflection groups. We also study the "poor man's essential dimension" of an arbitrary finite group, an intermediate notion between the absolute essential dimension and the essential dimension at a prime p.