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

. 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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