Elementary construction of the minimal free resolution of the Specht ideal of shape $(n-d,d)$

Abstract

Let $K$ be a field with $\mathrm{char}(K)=0$. For a partition $\lambda$ of $n\in \mathbb{N}$, let $I_{\lambda }^{\mathrm{Sp}}$ be the ideal of $R=K[x_1,\dots ,x_n]$ generated by all Specht polynomials of shape $\lambda$. These ideals have been studied from several points of view (and under several names). Using advanced tools of the representation theory, Berkesch Zamaere et al [BGS]. constructed a minimal free resolution of $I_{(n-d,d)}^{\mathrm{Sp}}$ except differential maps. The present paper constructs the differential maps, and also gives an elementary proof of the result of [BGS].

arXiv commentNo mathematical improvement, but exposition largely revised, especially, the title modified. 20 pages. Comments welcome