Equivariant Chern character operators and Okounkov's conjecture
Abstract
In this paper, we study the Chern character operators on the equivariant cohomology of the Hilbert schemes of points in the complex affine plane $\mathbb{C}^2$ with the action of the torus $\mathbb{T}=\left(\mathbb{C}^*\right)^2$, and partially verify Okounkov's Conjecture [33, Conjecture 2] in this setting. Our main idea is to apply the connection between the equivariant cohomology of these Hilbert schemes and the ring of symmetric functions, (the integral form of) the Jack symmetric functions and the transformed Macdonald symmetric functions [17, 20].
Fields of Study & Subjects
Advanced Operator Algebra Research
Spectral Theory in Mathematical Physics
Medical Imaging Techniques and Applications
Publication details
- Journal / source
- Pure and Applied Mathematics Quarterly
- Publisher
- International Press of Boston
- Volume
- 22
- Issue
- 3
- Pages
- 1075–1113
- Publication date
- 1 January 2026
- Language
- EN