Stability of Schur Functors, Original Research Article

Symplectic (resp. orthogonal) Schur functors are defined on a vector spaceVwith a non-degenerate skew-symmetric (resp. symmetric) bilinear form. Each of these functors determines an irreducible representation of imageimage(V) (resp. imageimage(V)). We prove that if dim Vis sufficiently large, then the splitting into irreducible components of the composition of a symplectic (orthogonal) Schur functor and an ordinary Schur functor applied toVis independent of dim V. We also prove the stability of the branching for the symplectic (orthogonal) Schur functors.