IJPAM: Volume 86, No. 3 (2013)
THE SCHUR FUNCTOR OF A VECTOR BUNDLE
Dipartimento di Matematica e Informatica ``U. Dini''
Viale Morgagni 67/A, 50134, Firenze, ITALY
Abstract. We prove that, for any complex vector bundle E of rank e on a compact Kähler manifold X, we have that μ (Sλ E) = |λ | μ(E) for any λ=(λ1, ...,λe-1) with λi ∈ N and λ1 ≥ ... ≥ λe-1, where |λ|= λ1+ ...+λe-1, the symbol Sλ 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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DOI: 10.12732/ijpam.v86i3.6 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395