Regularity of Cohen-Macaulay Specht ideals

Kosuke Shibata, Kohji Yanagawa

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

For a partition λ of n∈N, let IλSp be the ideal of R=K[x1,…,xn] generated by all Specht polynomials of shape λ. In the previous paper, the second author showed that if R/IλSp is Cohen-Macaulay, then λ is either (n−d,1,…,1),(n−d,d), or (d,d,1), and the converse is true if char(K)=0. In this paper, we compute the Hilbert series of R/IλSp for λ=(n−d,d) or (d,d,1). Hence, we get the Castelnuovo-Mumford regularity of R/IλSp, when it is Cohen-Macaulay. In particular, I(d,d,1)Sp has a (d+2)-linear resolution in the Cohen–Macaulay case.

Original languageEnglish
Pages (from-to)73-87
Number of pages15
JournalJournal of Algebra
Volume582
DOIs
Publication statusPublished - Sep 15 2021

Keywords

  • Cohen–Macaulay ring
  • Specht ideal
  • Specht polynomial
  • Subspace arrangement

ASJC Scopus subject areas

  • Algebra and Number Theory

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