Generalized invariants of reflection groups in rank two

TL;DR

This paper computes stable and generalized invariants for subgroups of GL_2(F_p) generated by reflections, linking algebraic invariants to the cohomology of various Lie and Kac-Moody groups.

Contribution

It provides explicit descriptions of invariants for reflection-generated subgroups in rank two, extending understanding of their algebraic and topological properties.

Findings

Computed ideals of stable invariants for specific subgroups

Connected invariants to cohomology of Lie and Kac-Moody groups

Extended classical invariant theory to generalized invariants in rank two

Abstract

For each subgroup of GL_2(F_p) or order divisible by p, generated by (pseudo-)reflections, we compute the ideals of stable and generalized invariants. These groups and these ideals are related to the cohomology of compact Lie groups, Kac-Moody groups and p-compact groups.