ON THE SLOPE OF THE SCHUR FUNCTOR OF A VECTOR BUNDLE

Abstract

We prove that, for any complex vector bundle E of rank e on a compact Kahler manifold X, we have that μ(SE) = |λ| μ(E) for any λ = (λ1, ..., λe−1) with λi ∈ N and λ1 ≥ ... ≥ λe−1, where |λ| = λ1 + ... + λe−1, the symbol S denotes the Schur functor and μ is the slope. This result has already been stated, without proof, by Ottaviani in 1995. AMS Subject Classification: 19L10, 55R10