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An action of the affine Yangian Yt1,t2(gl̂1) on the cohomology of the moduli space of stable sheaves on surfaces
Abstract
We investigate the action of the affine Yangian Yt1,t2(gl̂1) on the singular cohomology of the moduli space of stable sheaves ℳ on a smooth projective surface S. Through an intersection-theoretic analysis of nested moduli spaces, we obtain a proof of the representation Yt1,t2(gl̂1) curvearrowright Hℳ. This intersection-theoretic approach extends classical constructions to the full Yangian structure and circumvents the K-theoretic machinery traditionally required to establish this action.
Related
- PBW theorem for affine super Yangian
- Cohomology of integral structure sheaves for open varieties
- The Serre-Grothendieck Finiteness Theorem for the cohomology of coherent sheaves
- Stability of representation cohomology sheaves on moduli spaces of bundles
- Limits of Hyperkähler Manifolds and Moduli Spaces of Sheaves on K3 Surfaces
BibTeX
@misc{pfammatter2026action,
title = {{An action of the affine Yangian $Y_t_1,t_2(\widehat\mathfrakgl_1)$ on the cohomology of the moduli space of stable sheaves on surfaces}},
author = {Claudio Pfammatter},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.27473},
eprint = {2608.27473},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.27473},
}
RIS
TY - UNPB
TI - An action of the affine Yangian Y_t_1,t_2(gl̂_1) on the cohomology of the moduli space of stable sheaves on surfaces
AU - Claudio Pfammatter
PY - 2026
DA - 2026/08/19
PB - arXiv
DO - 10.48550/arxiv.2608.27473
UR - https://arxiv.org/abs/2608.27473
AB - We investigate the action of the affine Yangian Y_t_1,t_2(gl̂_1) on the singular cohomology of the moduli space of stable sheaves ℳ on a smooth projective surface S. Through an intersection-theoretic analysis of nested moduli spaces, we obtain a proof of the representation Y_t_1,t_2(gl̂_1) curvearrowright H_ℳ. This intersection-theoretic approach extends classical constructions to the full Yangian structure and circumvents the K-theoretic machinery traditionally required to establish this action.
ER -