Papers › The second cohomology of regular semisimple Hessenberg varieties from GKM theory
The second cohomology of regular semisimple Hessenberg varieties from GKM theory
Anton Ayzenberg, Mikiya Masuda, Takashi Sato
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We describe the second cohomology of a regular semisimple Hessenberg variety by generators and relations explicitly in terms of GKM theory. The cohomology of a regular semisimple Hessenberg variety becomes a module of a symmetric group 𝔖ₙ by the dot action introduced by Tymoczko. As an application of our explicit description, we give a formula describing the isomorphism class of the second cohomology as an 𝔖ₙ-module. Our formula is not exactly the same as the known formula by Chow or Cho-Hong-Lee but they are equivalent. We also discuss its higher degree generalization.
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