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

2022/05/11 by Gui, Tao
#Algebraic Topology (math.AT) #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2205.05408

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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