Geometric proofs of horn and saturation conjectures

By P. Belkale. 2002

83 citations recorded by the source corpus.

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"

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/429fcf2e8e2346425a7e49d636e620938bf07829

Citations in the corpus

• An Invitation to the Generalized Saturation Conjecture (2004, unknown): “) 6= 0 ⇔N(λ −µ) ∈Y η ⇔λ−µ ∈Y η ⇔d(λ,µkη) 6= 0 . Now let us explain briefly a connection between our Generalized Saturation Conjecture and the Saturation Theorem by A. Knutson and T. Tao [43], see also [4], [9], [14], [65] for other proofs. Theorem 1.4 ( Saturation Theorem [43] ) Let λ,µ and ν be part”
• The combinatorics of quiver representations (2006, unknown): “4 was given by the authors in [11] and by Belkale in [1].”