1999/04/26 by Michel Brion, Brion, Michel, Patrick Polo +1
Mathematics · #14L30 #14M15 #19E15 #20G05 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Representation Theory (math.RT) #math.AG #math.RT #msc:14L30 #msc:14M15 #msc:19E15 #msc:20G05
paper · pdf · doi:10.48550/arxiv.math/9904144
33 pages, LaTeX2e
arxiv created 1999/04/26 · openalex publication_date 1999/04/26 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31
For a semisimple adjoint algebraic group G and a Borel subgroup B, consider the double classes BwB in G and their closures in the canonical compactification of G: we call these closures large Schubert varieties. We show that these varieties are normal and Cohen-Macaulay; we describe their Picard group and the spaces of sections of their line bundles. As an application, we construct geometrically van der Kallen's filtration of the algebra of regular functions on B. We also construct a degeneration of the flag variety G/B embedded diagonally in G/B× G/B, into a union of Schubert varieties. This leads to formulae for the class of the diagonal in T-equivariant K-theory of G/B× G/B, where T is a maximal torus of B.