Wreath Macdonald operators
Abstract We construct a novel family of difference-permutation operators and prove that they are diagonalized by the wreath Macdonald P -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.
Authors
- Daniel L. Orr (ORCID: https://orcid.org/0000-0002-2347-4693)
- Mark Shimozono (ORCID: https://orcid.org/0000-0002-9647-3229)
- Joshua Jeishing Wen (ORCID: https://orcid.org/0000-0002-5800-4165)
Institutions
- University of Vienna (AT)
- Max Planck Institute for Mathematics (DE)
- Virginia Tech (US)
Publication Details
- Journal
- Forum of Mathematics Sigma
- Published
- 2025-01-01
- DOI
- https://doi.org/10.1017/fms.2025.10061
- Primary Topic
- Matrix Theory and Algorithms
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- National Science Foundation
- Simons Foundation