On the spectral properties of the quantum cohomology of odd quadrics

Let $H^{\bullet }(OG)$ be the quantum cohomology (specialized at $q=1$) of the $2n-1$ dimensional quadric $OG$. We will calculate the characteristic polynomial of the linear operators induced by quantum multiplication in $H^{\bullet }(OG)$ and the Frobenius-Perron dimension. We also check that Galkin’s lower bound conjecture holds for $OG$.