Lefschetz Properties and Perfection of Specht Ideals of Two-Rowed Partitions.

We prove, among other things, that the Specht ideal of a two-rowed partition is perfect over an arbitrary field, provided that the characteristic is either zero or large enough with respect to certain numerical parameters of the ideal. In particular we give a self-contained proof of Cohen-Macaulayness of the so-called $h$-equals set, a result previously obtained by Etingof-Gorsky-Losev over the complex numbers using rational Cherednik algebras.