Fourier-Deligne transform and representations of the symmetric group

Galyna Dobrovolska
2013 Mathematical Research Letters  
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 » ... λ of S k , the Young 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.
doi:10.4310/mrl.2013.v20.n6.a5 fatcat:taavs7tjmrdurjf6ddz2tl7jxi