主Radical系统、Lefschetz性质和双列分拆的Specht理想的完善性
Principal Radical Systems, Lefschetz Properties and Perfection of Specht Ideals of Two-Rowed Partitions
摘要：
我们表明，Specht理想的两行分区是完美的任意字段，提供的特征是零或有界的第二行的分区的大小，我们表明这个下界是紧的。我们还建立完善和其他性质的某些变种的Specht理想，并发现一个令人惊讶的连接到弱Lefschetz属性。我们的结果特别给出了一个自包含的证明科恩-Macaulayness某些$h$ -等于集，一个结果先前获得的Etingof-Gorsky-Losev在复数使用合理的Cherednik代数。
英文摘要：
We show that the Specht ideal of a two-rowed partition is perfect over an arbitrary field, provided that the characteristic is either zero or bounded below by the size of the second row of the partition, and we show this lower bound is tight. We also establish perfection and other properties of certain variants of Specht ideals, and find a surprising connection to the weak Lefschetz property. Our results in particular give a self-contained proof of Cohen-Macaulayness of certain $h$-equals sets, a result previously obtained by Etingof-Gorsky-Losev over the complex numbers using rational Cherednik algebras.
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