Eigenvalues of Heckman–Polychronakos operators
Year: 2026
Type: article
Abstract: Heckman–Polychronakos operators form a prominent family of commuting differential-difference operators defined in terms of the Dunkl operators 𝒟 i as 𝒫 m = ∑ i = 1 N ( x i 𝒟 i ) m . They have been known since 1990s in connection with trigonometric Calogero–Moser–Sutherland Hamiltonian and Jack symmetric polynomials. We explicitly compute the eigenvalues of these operators for symmetric and skew-symmetric eigenfunctions, as well as partial sums of eigenvalues for general polynomial eigenfunctions.
Source: Algebraic Combinatorics
DOI: 10.5802/alco.451
Authors: Charles Dunkl, Vadim Gorin
Institutions: University of Virginia, University of California, Berkeley
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W7119033243