Steven Sam: Saturation theorems for the classical groups


Abstract

Following Klyachko's solution of Horn's problem of characterizing the eigenvalues of A+B in terms of the eigenvalues of Hermitian matrices A and B, there has been interest in the so-called saturation conjecture (now theorem). This says that c^nu_{lambda, mu} > 0 if and only if c^{N*nu}_{N*lambda, N*mu} > 0 for some N>0 where c is the Littlewood-Richardson coefficient. Following work of Derksen-Weyman and Schofield, I proved a generalization of this statement for orthogonal and symplectic groups. I will explain the problem and go through the main ideas of the proof.