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Winter 2021 When is a Specht ideal Cohen–Macaulay?
Kohji Yanagawa
J. Commut. Algebra 13(4): 589-608 (Winter 2021). DOI: 10.1216/jca.2021.13.589

Abstract

For a partition λ of n, let IλSp be the ideal of R=K[x1,,xn] generated by all Specht polynomials of shape λ. We show that if RIλSp 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 in the char(K)=0 case. To show the latter statement, the radicalness of these ideals and a result of Etingof et al. are crucial. We also remark that RI(n3,3)Sp is not Cohen–Macaulay if and only if char(K)=2.

Citation

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Kohji Yanagawa. "When is a Specht ideal Cohen–Macaulay?." J. Commut. Algebra 13 (4) 589 - 608, Winter 2021. https://doi.org/10.1216/jca.2021.13.589

Information

Received: 29 March 2019; Revised: 1 July 2019; Accepted: 3 July 2019; Published: Winter 2021
First available in Project Euclid: 18 January 2022

Digital Object Identifier: 10.1216/jca.2021.13.589

Subjects:
Primary: 13F99

Keywords: Cohen–Macaulay ring , Specht ideal , Specht polynomial , subspace arrangement

Rights: Copyright © 2021 Rocky Mountain Mathematics Consortium

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Vol.13 • No. 4 • Winter 2021
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