On semidualizing modules of ladder determinantal rings

We identify all semidualizing modules over certain classes of ladder determinantal rings over a field $\mathsf{k}$. Specifically, given a ladder of variables $Y$, we show that the ring $\mathsf{k}[Y]\mathrm{/}{I}_t(Y)$ has only trivial semidualizing modules up to isomorphism in the following cases: (1) $Y$ is a one-sided ladder, and (2) $Y$ is a two-sided ladder with $t=2$ and no coincidental inside corners.