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We show that the Specht ideal of a two-rowed partition is perfect over anarbitrary field, provided that the characteristic is either zero or boundedbelow by the size of the second row of the partition, and we show this lowerbound is tight. We also establish perfection and other properties of certainvariants of Specht ideals, and find a surprising connection to the weakLefschetz property. Our results in particular give a self-contained proof ofCohen-Macaulayness of certain $h$-equals sets, a result previously obtained byEtingof-Gorsky-Losev over the complex numbers using rational Cherednikalgebras.

Principal Radical Systems, Lefschetz Properties and Perfection of Specht Ideals of Two-Rowed Partitions