Block Basis for Coinvariants of Modular Pseudo-reflection Groups

TL;DR

This paper explores the structure of coinvariants in modular pseudo-reflection groups, focusing on block bases for groups related to parabolic subgroups of GL_n(q), extending previous work in the area.

Contribution

It introduces a new approach to understanding coinvariants of modular pseudo-reflection groups, especially those linked to parabolic subgroups of GL_n(q).

Findings

Established block basis structures for specific modular pseudo-reflection groups.

Extended the theory to groups generalizing Weyl groups of restricted Cartan type Lie algebras.

Provided new insights into the algebraic properties of coinvariants in modular settings.

Abstract

As a sequel of \cite{Ou}, in this shot note, we investigate block basis for coinvariants of finite modular pseudo-reflection groups. We are particularly interested in the case where $ G $ is a subgroup of the parabolic subgroups of $ GL_n(q) $ which generalizes the Weyl groups of restricted Cartan type Lie algebra.