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arXiv · 2607.03284

Permutation module decomposition of the cohomology of Hessenberg varieties associated with lollipop graphs

Soojin Cho·Seonjeong Park
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Abstract

We study the cohomology of regular semisimple Hessenberg varieties associated with lollipop graphs as a module under the dot action. Using the natural basis introduced by Cho, Hong, and Lee, which we call the CHL basis, we establish structural properties of the dot action, including a result for classes satisfying \(i\)-decomposability. We also obtain an explicit elementary symmetric function expansion of the chromatic quasisymmetric functions of lollipop graphs in terms of \(h\)-admissible permutations and their associated partitions. Combining these geometric and combinatorial results, we construct a permutation module decomposition of the cohomology of the corresponding Hessenberg varieties, thereby proving a conjecture of Cho, Hong, and Lee for lollipop graphs.

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Soojin Cho, Seonjeong Park. 2026-07-03. Permutation module decomposition of the cohomology of Hessenberg varieties associated with lollipop graphs. https://arxiv.org/abs/2607.03284

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