Guo–Zeng's gamma-positivity conjecture for involution polynomials

For each positive integer $n$, let $I_n(x)$ denote the polynomial defined by the paper through the descent enumerator of standard Young tableaux with $n$ squares. Guo–Zeng's conjecture. The polynomial $I_n(x)$ is $\gamma$-positive for every positive integer $n$. This conjecture strengthens the known symmetry and unimodality of $I_n(x)$; the source states that it remains open, although these polynomials are not real-rooted, and not even log-concave for sufficiently large $n$.