Quantum Corner Polynomials: A Generalization of Super Macdonald Polynomials and Their VOA Correspondence

TL;DR

This paper introduces quantum corner polynomials, generalizing super Macdonald polynomials, and establishes their connection to quantum corner VOAs, providing proofs of their partial symmetricity.

Contribution

It presents a new family of partially symmetric polynomials and links them to quantum corner VOAs, extending the theory of super Macdonald polynomials.

Findings

Quantum corner polynomials generalize super Macdonald polynomials.

They correspond precisely to quantum corner VOAs.

The partial symmetricity of these polynomials is rigorously proven.

Abstract

In this paper, we introduce a family of partially symmetric polynomials, which we call quantum corner polynomials, as a generalization of the Sergeev-Veselov super Macdonald polynomials. We show that these quantum corner polynomials are precisely the partially symmetric polynomials corresponding to the quantum corner VOAs. Furthermore, we provide a detailed proof of the partial symmetricity of these polynomials.