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Abstract The goal of this paper is to better understand the quasimap vertex functions of typeANakajima quiver varieties. To that end, we construct an explicit embedding of any typeAquiver variety into a typeAquiver variety with all framings at the rightmost vertex of the quiver. Then, we consider quasimap counts, showing that the map induced by this embedding on equivariantK-theory preserves vertex functions.
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This content will become publicly available on June 1, 2026
Capped vertex functions for $${\text {Hilb}}^n(\mathbb {C}^2)$$
We obtain explicit formulas for the K-theoretic capped descendent vertex functions of $${\text {Hilb}}^n(\mathbb {C}^2)$$ for descendents given by the exterior algebra of the tautological bundle. This formula provides a one-parametric deformation of the generating function for normalized Macdonald polynomials. In particular, we show that the capped vertex functions are rational functions of the quantum parameter.
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- Award ID(s):
- 2401380
- PAR ID:
- 10589488
- Publisher / Repository:
- Springer
- Date Published:
- Journal Name:
- Letters in Mathematical Physics
- Volume:
- 115
- Issue:
- 3
- ISSN:
- 1573-0530
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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