Haglund's conjecture for multi-$t$ Macdonald polynomials

TL;DR

This paper introduces new methods to prove identities involving modified Macdonald polynomials using LLT expansions, and confirms Haglund's conjecture for multi-$t$-Macdonald polynomials with two rows.

Contribution

It presents novel approaches to prove identities for modified Macdonald polynomials and verifies Haglund's conjecture for a specific class of multi-$t$-Macdonald polynomials.

Findings

Proved identities for modified Macdonald polynomials using LLT expansions.

Confirmed Haglund's conjecture for two-row multi-$t$-Macdonald polynomials.

Abstract

We provide new approaches to prove identities for the modified Macdonald polynomials via their LLT expansions. As an application, we prove a conjecture of Haglund concerning the multi-$t$-Macdonald polynomials of two rows.