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arXiv · 2205.05408

On the equivariant log-concavity for the cohomology of the flag varieties

Tao Gui
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Abstract

We study the $S_n$-equivariant log-concavity of the cohomology of flag varieties, also known as the coinvariant ring of $S_n$. Using the theory of representation stability, we give computer-assisted proofs of the equivariant log-concavity in low degrees and high degrees and conjecture that it holds for all degrees. Furthermore, we make a stronger unimodal conjecture which implies the equivariant log-concavity.

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Tao Gui. 2022-05-11. On the equivariant log-concavity for the cohomology of the flag varieties. https://arxiv.org/abs/2205.05408

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