Abstract. We prove that, for any complex vector bundle E of rank e on a compact Kähler manifold X, we have that μ (S^λ E) = |λ | μ(E) for any λ=(λ₁, ...,λ_e-1) with λ_i ∈ N and λ₁ ≥ ... ≥ λ_e-1, where |λ|= λ₁+ ...+λ_e-1, the symbol S^λ denotes the Schur functor and μ is the slope. This result has already been stated, without proof, by Ottaviani in 1995.

Received: March 20, 2013

AMS Subject Classification: 19L10, 55R10

Key Words and Phrases: slope, Schur functors

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