A geometric realization of partially-symmetric Macdonald polynomials
Year: 2026
Type: article
Abstract: We formulate a precise conjecture relating integral form partially-symmetric Macdonald polynomials and the parabolic flag Hilbert schemes of Carlsson, Gorsky, and Mellit. This extends, in an explicit fashion, Haiman's realization of modified Macdonald symmetric functions via Hilbert schemes of points in the plane. As evidence for our conjecture we prove that it is compatible with the action of certain elements in Carlsson and Mellit's algebra \(\mathbb{A}_{t,q}\), including degree \(1\) Pieri formulas. Mathematics Subject Classifications: 05E10, 05E05 Keywords: Macdonald polynomials, Hilbert schemes, Hecke algebras
Source: Combinatorial Theory
DOI: 10.5070/c6.68699
Authors: Ben Goodberry, Daniel Orr
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4390041431