A GKM Description of the Equivariant Coinvariant Ring of a Pseudo Reflection Group

TL;DR

This paper characterizes the equivariant coinvariant ring of a pseudo-reflection group using GKM theory, linking algebraic structures to geometric models via hypergraph cohomology.

Contribution

It provides a novel GKM description of the equivariant coinvariant ring for pseudo-reflection groups, connecting algebraic and geometric perspectives.

Findings

Equivariant coinvariant ring is identified with its localization image.

The image can be realized as equivariant cohomology of a linear hypergraph.

Establishes a GKM framework for pseudo-reflection groups.

Abstract

We identify the equivariant coinvariant ring of a pseudo-reflection group with its image under the localization map. We then show that this image can be realized as the equivariant cohomology of a sort linear hypergraph, analogous to a GKM 1-skeleton.