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
SN - 0021-8693
VL - 582
SP - 73
EP - 87
JO - Journal of Algebra
JF - Journal of Algebra
ER -