A proof of the compositional Delta conjecture

TL;DR

This paper proves a refined version of the Delta conjecture related to symmetric functions, specifically addressing a compositional aspect of the rise version, advancing understanding in algebraic combinatorics.

Contribution

It provides a proof of a compositional refinement of the Delta conjecture for the symmetric function $ abla_{e_{n-k-1}}' e_n$, connecting Theta operators and combinatorial conjectures.

Findings

Proof of the compositional Delta conjecture (rise version)

Connection established between Theta operators and symmetric functions

Advancement in algebraic combinatorics understanding

Abstract

We prove a compositional refinement of the Delta conjecture (rise version) of Haglund, Remmel and Wilson (2018) for $\Delta_{e_{n-k-1}}'e_n$ which was stated by D'Adderio, Iraci and Vanden Wyngaerd (2020) in terms of Theta operators.