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arXiv · 2310.16235

Modular law through GKM theory

Tatsuya Horiguchi·Mikiya Masuda·Takashi Sato
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Abstract

The solution of Shareshian-Wachs conjecture by Brosnan-Chow and Guay-Paquet tied the graded chromatic symmetric functions on indifference graphs (or unit interval graphs) and the cohomology of regular semisimple Hessenberg varieties with the dot action. A similar result holds between unicellular LLT polynomials and twins of regular semisimple Hessenberg varieties. A recent result by Abreu-Nigro enabled us to prove these results by showing the modular law for the geometrical objects, and this is indeed done by Precup-Sommers and Kiem-Lee. In this paper, we give elementary and simpler proofs to the modular law through GKM theory.

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Tatsuya Horiguchi, Mikiya Masuda, Takashi Sato. 2023-10-24. Modular law through GKM theory. https://arxiv.org/abs/2310.16235

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