Geometric Proofs of Horn and Saturation Conjectures

Abstract

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"

36 pages, accepted for publication in the Journal of Algebraic Geometry

References in corpus (2)

• The honeycomb model of GL(n) tensor products II: Puzzles determine facets of the Littlewood-Richardson cone
• Transformation formulas in Quantum Cohomology

Cited by in corpus (8)

• Geometric Complexity Theory VI: the flip via saturated and positive integer programming in representation theory and algebraic geometry
• Tensor product decompositions and open orbits in multiple flag varieties
• An Invitation to the Generalized Saturation Conjecture
• Geometric Complexity Theory: Introduction
• Irredundance in Eigenvalue Problems
• Self maps of P^1 with prescribed ramification in characteristic p
• Exterior differential algebras and flat connections on Weyl groups
• The Horn recursion for Schur P- and Q- functions: Extended Abstract