Document Type


Publication Date


Publication Title

La Matematica


Recent work of Shareshian and Wachs, Brosnan and Chow, and Guay-Paquet connects the wellknown Stanley–Stembridge conjecture in combinatorics to the dot action of the symmetric group Sn on the cohomology rings H∗ (Hess(S, h)) of regular semisimple Hessenberg varieties. In particular, in order to prove the Stanley–Stembridge conjecture, it suffices to construct (for any Hessenberg function h) a permutation basis of H∗ (Hess(S, h)) whose elements have stabilizers isomorphic to Young subgroups. In this manuscript we give several results which contribute toward this goal. Specifically, in some special cases, we give a new, purely combinatorial construction of classes in the T-equivariant cohomology ring H∗ T (Hess(S, h)) which form permutation bases for subrepresentations in H∗ T (Hess(S, h)). Moreover, from the definition of our classes it follows that the stabilizers are isomorphic to Young subgroups. Our constructions use a presentation of the T-equivariant cohomology rings H∗ T (Hess(S, h)) due to Goresky, Kottwitz, and MacPherson. The constructions presented in this manuscript generalize past work of Abe–Horiguchi–Masuda, Chow, and Cho–Hong–Lee.



First Page


Last Page


Creative Commons License

Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.


Licensed to Smith College and distributed CC-BY under the Smith College Faculty Open Access Policy.


Peer reviewed accepted manuscript.

Included in

Mathematics Commons



To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.