Representation theory and the diagonal coinvariant ring of the type B Weyl group

TL;DR

This paper uses representation theory to establish a new lower bound on the dimension of the type B Weyl group diagonal coinvariant ring, surpassing previous bounds with a quadratic polynomial improvement.

Contribution

It introduces a novel representation-theoretic approach to improve the known lower bounds for the dimension of the type B diagonal coinvariant ring.

Findings

New quadratic lower bound on the dimension

Improved understanding of type B diagonal invariants

Enhanced techniques for bounding coinvariant ring dimensions

Abstract

We explain how to use representation theory to give a lower bound on the dimension of the quotient ring by type $B_n$ diagonal invariants that improves upon the current known lower bound $(2n+1)^n$ by a quadratic polynomial in $n$.