TY - JOUR

T1 - Regularity of Cohen-Macaulay Specht ideals

AU - Shibata, Kosuke

AU - Yanagawa, Kohji

N1 - Funding Information:
The second author is partially supported by JSPS Grant-in-Aid for Scientific Research (C) 19K03456.
Publisher Copyright:
© 2021 Elsevier Inc.

PY - 2021/9/15

Y1 - 2021/9/15

N2 - 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.

AB - 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.

KW - Cohen–Macaulay ring

KW - Specht ideal

KW - Specht polynomial

KW - Subspace arrangement

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U2 - 10.1016/j.jalgebra.2021.04.022

DO - 10.1016/j.jalgebra.2021.04.022

M3 - Article

AN - SCOPUS:85105585413

VL - 582

SP - 73

EP - 87

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

ER -