Wreath Macdonald operators
Quantum Algebra
2025-09-16 v3 Combinatorics
Representation Theory
Abstract
We construct a novel family of difference-permutation operators and prove that they are diagonalized by the wreath Macdonald -polynomials; the eigenvalues are written in terms of elementary symmetric polynomials of arbitrary degree. Our operators arise from integral formulas for the action of the horizontal Heisenberg subalgebra in the vertex representation of the corresponding quantum toroidal algebra
Cite
@article{arxiv.2211.03851,
title = {Wreath Macdonald operators},
author = {Daniel Orr and Mark Shimozono and Joshua Jeishing Wen},
journal= {arXiv preprint arXiv:2211.03851},
year = {2025}
}
Comments
v3, 54pp. Added more clarifications and improved exposition in response to referee's comments. Final version