Elementary construction of minimal free resolutions of the Specht ideals of shapes (n−2,2) and (d,d,1)

Shibata Kosuke; Yanagawa Kohji

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Elementary construction of minimal free resolutions of the Specht ideals of shapes (n−2,2) and (d,d,1)

机译：Elementary construction of minimal free resolutions of the Specht ideals of shapes (n−2,2) and (d,d,1)

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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. We assume that char(K)=0. Then R/I(n−2,2)Sp is Gorenstein, and R/I(d,d,1)Sp is a Cohen–Macaulay ring with a linear free resolution. In this paper, we construct minimal free resolutions of these rings. Zamaere et al. [Jack polynomials as fractional quantum Hall states and the Betti numbers of the (k+1)-equals ideal, Commun. Math. Phys. 330 (2014) 415–434] already studied minimal free resolutions of R/I(n−d,d)Sp, which are also Cohen–Macaulay, using highly advanced technique of the representation theory. However, we only use the basic theory of Specht modules, and explicitly describe the differential maps.

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《Journal of algebra and its applications》 |2023年第9期|共26页
作者
Shibata Kosuke; Yanagawa Kohji;
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作者单位

Department of Mathematics, Okayama University, Okayama, Okayama 700-8530,Japan;

Department of Mathematics, Kansai University, Suita, Osaka 564-8680,Japan;

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正文语种英语
中图分类代数、数论、组合理论;
关键词
Specht polynomial; Specht ideal; minimal free resolution; Cohen–Macaulay ring;

Elementary construction of minimal free resolutions of the Specht ideals of shapes (n−2,2) and (d,d,1)

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