When is a Specht ideal Cohen-Macaulay?

2019/02/18 by Yanagawa, Kohji · 1 citation
#13F99 #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1902.06577

Abstract

For a partition λ of n, let I^{\rm Sp}_λ be the ideal of R=K[x₁, …, x_n] generated by all Specht polynomials of shape λ. We show that if R/I^{\rm Sp}_λ is Cohen--Macaulay then λ is of the form either (a, 1, …, 1), (a,b), or (a,a,1). We also prove that the converse is true if \rm char(K)=0. To show the latter statement, the radicalness of these ideals and a result of Etingof et al. are crucial. We also remark that R/I^{\rm Sp}_(n-3,3) is NOT Cohen--Macaulay if and only if \rm char(K)=2.

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