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For a partition $\lambda$ of $n \in \mathbb{N}$, let $I^{\rm Sp}_\lambda$ bethe ideal of $R=K[x_1,\ldots,x_n]$ generated by all Specht polynomials of shape$\lambda$. We assume that ${\rm char}(K)=0$. Then $R/I^{\rm Sp}_{(n-2,2)}$ isGorenstein, and $R/I^{\rm Sp}_{(d,d,1)}$ is a Cohen-Macaulay ring with a linearfree resolution. In this paper, we construct minimal free resolutions of theserings. Berkesch Zamaere, Griffeth, and Sam had already studied minimal freeresolutions of $R/I^{\rm Sp}_{(n-d,d)}$, which are also Cohen-Macaulay, usingheighly advanced technique of the representation theory. However we only usethe basic theory of Specht modules, and explicitly describe the differentialmaps.

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