Young diagrams and intersection numbers for toric manifolds associated with Weyl chambers

2014/04/15 by Hiraku Abe, Abe, Hiraku · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1404.3805

openalex publication_date 2014/04/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study intersection numbers of invariant divisors in the toric manifold associated with the fan determined by the collection of Weyl chambers for each root system of classical type and of exceptional type G₂. We give a combinatorial formula for intersection numbers of certain subvarieties which are naturally indexed by elements of the Weyl group. These numbers describe the ring structure of the cohomology of the toric manifold.

Citations

• Some Permutation Representations of Weyl Groups Associated with the Cohomology of Toric Varieties

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