Geometric Proofs of Horn and Saturation Conjectures

We provide a geometric proof of the Schubert calculus interpretation of the Horn conjecture, and show how the saturation conjecture follows from it. The geometric proof gives a strengthening of Horn and saturation conjectures. We also establish transversality theorems for Schubert calculus in non-zero characteristic. Some parts of the version posted in Nov 2002 (concerning explicit invariants constructed from Schubert calculus) have been removed from this version. They have appeared separately in IMRN 2004, no. 69, pages 3709--3721 " Invariant theory of GL(n) and Intersection theory of Grassmannians"Comment: 36 pages, accepted for publication in the Journal of Algebraic Geometr

Geometric Proof of a Conjecture of Fulton

We give a geometric proof of a conjecture of W. Fulton on the multiplicities of irreducible representations in a tensor product of irreducible representations for GL(r).Comment: 10 pages, no figure