A module for the Delta conjecture

TL;DR

This paper introduces a new module extending diagonal harmonics, aiming to realize the symmetric function in the Delta conjecture through its graded Frobenius characteristic.

Contribution

It defines a novel module that potentially confirms the symmetric function expression in the Delta conjecture, advancing understanding in algebraic combinatorics.

Findings

Proposes a module extension of diagonal harmonics

Conjectures the module's Frobenius characteristic matches the Delta conjecture expression

Provides a framework for future proof of the conjecture

Abstract

We define a module that is an extension of the diagonal harmonics and whose graded Frobenius characteristic is conjectured to be the symmetric function expression which appears in `the Delta conjecture' of Haglund, Remmel and Wilson [arXiv:1509.07058].