We calculate the Fourier-Deligne transform of the IC extension to C n+1 of the local system L Λ on the cone over Conf n (P 1 ) associated with a representation Λ of the symmetric group S n , where the length n − k of the first row of the Young diagram of Λ is at least 2 . The answer is the IC extension to the dual vector space C n+1 of the local system R λ on the cone over the kth secant variety of the rational normal curve in P n , where R λ corresponds to the representation λ of S k , the

more »

... g diagram of which is obtained from the Young diagram of Λ by deleting its first row. We also prove an analogous statement for S n -local systems on fibers of the Abel-Jacobi map. We use our result on the Fourier-Deligne transform to rederive a part of a result of Michel Brion on Kronecker coefficients.