Affine Pavings of Hessenberg Ideal Fibers
Abstract
We define certain closed subvarieties of the flag variety, Hessenberg ideal fibers, and prove that they are paved by affines. Hessenberg ideal fibers are a natural generalization of Springer fibers. In type , we give explicit descriptions of all Hessenberg ideal fibers, study some of their geometric properties and use them to completely classify Tymoczko's dot actions of the Weyl group on the cohomology of regular semisimple Hessenberg varieties.
Cite
@article{arxiv.2007.08712,
title = {Affine Pavings of Hessenberg Ideal Fibers},
author = {Ke Xue},
journal= {arXiv preprint arXiv:2007.08712},
year = {2024}
}
Comments
[v4] adds recent related works and citations of this paper. [v3] improves Lemma 2.5 to a new version that achieves the same result from a weaker assumption. Proposition 2.13 is remade to show that Lemma 2.5 still applies to $\mathcal{O}_v$ even though it is not necessarily a vector bundle over $\mathcal{O}_v^{\lambda}$. [v2] added an accidentally omitted case of $U$ for type $F_4$ in section 6