Eigenvalues of Heckman–Polychronakos operators
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.
Fields of Study & Subjects
Holomorphic and Operator Theory
Approximation Theory and Sequence Spaces
Mathematical Analysis and Transform Methods
Publication details
- Journal / source
- Algebraic Combinatorics
- Volume
- 8
- Issue
- 6
- Pages
- 1547–1566
- Publication date
- 6 January 2026
- Language
- EN