2021/03/01 by Chris McDaniel, McDaniel, Chris, Junzo Watanabe +1 · 1 citation
Mathematics · #13A50 #13C14 #20C30 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2103.00759
openalex publication_date 2021/03/01 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
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.