English

Shuffle approach to wreath Pieri operators

Quantum Algebra 2025-09-16 v1 Combinatorics Representation Theory

Abstract

We describe a way to study and compute Pieri rules for wreath Macdonald polynomials using the quantum toroidal algebra. The Macdonald pairing can be naturally generalized to the wreath setting, but the wreath Macdonald polynomials are no longer collinear with their duals. We establish the relationship between these dual polynomials and the quantum toroidal algebra, and we outline a way to compute norm formulas. None of the aforementioned formulas are successfully computed in this paper.

Keywords

Cite

@article{arxiv.2402.06007,
  title  = {Shuffle approach to wreath Pieri operators},
  author = {Joshua Jeishing Wen},
  journal= {arXiv preprint arXiv:2402.06007},
  year   = {2025}
}

Comments

23 pages. To appear in Contemporary Mathematics. Comments welcome!

R2 v1 2026-06-28T14:43:26.320Z