2019/04/30 by Richárd Rimányi, Richard Rimanyi, Andrzej Weber · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic Geometry and Number Theory #Class (philosophy) #Elliptic curve #Equivariant map #Flag (linear algebra) #Recursion (computer science) #Resolution (logic) #Schubert calculus #Schubert polynomial #Schubert variety #math.AG #math.KT #math.RT #msc:14C17 #msc:14M15 #msc:19L47 #msc:55N34
paper · pdf · doi:10.1112/topo.12152
the paper has been accepted for publication by the Journal of Topology; this version contains minor corrections
openalex created_date 2020/03/27 · openalex publication_date 2020/05/14 · arxiv created 2020/06/09 · arxiv updated 2020/06/11 · openalex updated_date 2026/08/05
Based on recent advances on the relation between geometry and representation theory, we propose a new approach to elliptic Schubert calculus. We study the equivariant elliptic characteristic classes of Schubert varieties of the generalized full flag variety G / B . For this first we need to twist the notion of elliptic characteristic class of Borisov–Libgober by a line bundle, and thus allow the elliptic classes to depend on extra variables. Using the Bott–Samelson resolution of Schubert varieties we prove a BGG-type recursion for the elliptic classes, and study the Hecke algebra of our elliptic BGG operators. For G = GL n ( C ) we find representatives of the elliptic classes of Schubert varieties in natural presentations of the K theory ring of G / B , and identify them with the Tarasov–Varchenko weight function. As a byproduct we find another recursion, different from the known R-matrix recursion for the fixed point restrictions of weight functions. On the other hand the R-matrix recursion generalizes for arbitrary reductive group G.