2008/12/11 by Nicolas Ressayre, Ressayre, Nicolas · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #math.AG
paper · pdf · doi:10.48550/arxiv.0812.2122
The main result of this note was obtained simultenously by E. Richmond (see arXiv:0812.1856)
arxiv created 2008/12/11 · openalex publication_date 2008/12/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Consider a partial flag variety X which is not a grassmaninan. Consider also its cohomology ring \rm H^*(X,\ZZ) endowed with the base formed by the Poincaré dual classes of the Schubert varieties. In \citeRichmond:recursion, E. Richmond showed that some coefficient structure of the product in \rm H^*(X,\ZZ) are products of two such coefficients for smaller flag varieties. Consider now a quiver without oriented cycle. If α and β denote two dimension-vectors, α∘β denotes the number of α-dimensional subrepresentations of a general α+β-dimensional representation. In \citeDW:comb, H. Derksen and J. Weyman expressed some numbers α∘β as products of two smaller such numbers. The aim of this work is to prove two generalisations of the two above results by the same way.