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

Abstract

Let K be a field with char(K)=0. 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. 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. [1] constructed a minimal free resolution of I(n−d,d)Sp except differential maps. The present paper constructs the differential maps, and also gives an elementary proof of the result of [1].