2013/03/22 by Erik Carlsson, Carlsson, Erik
Mathematics · #14-xx #22-xx #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #math.RT #msc:14-xx #msc:22-xx
paper · pdf · doi:10.48550/arxiv.1303.5512
21 pages, no figures
openalex publication_date 2013/03/22 · arxiv created 2013/07/29 · arxiv updated 2013/07/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let X = \bigcupk Xk be the ind-Grassmannian of codimension n subspaces of an infinite-dimensional torus representation. If \cE is a bundle on X, we expect that ∑j (-1)j Λj(\cE) represents the K-theoretic fundamental class [\cOY] of a subvariety Y ⊂ X dual to \cE^*. It is desirable to lift a K-theoretic "projection formula" from the finite-dimensional subvarieties Xk, but such a statement requires switching the order of the limits in j and k. We find conditions in which this may be done, and consider examples in which Y is the Hilbert scheme of points in the plane, the Hilbert scheme of an irreducible curve singularity, and the affine Grassmannian of SL(2,\C). In the last example, the projection formula becomes an instance of the Weyl-Kaç character formula, which has long been recognized as the result of formally extending Borel-Weil theory and localization to Y \citeS. See also \citeC3 for a proof of the MacDonald inner product formula of type An along these lines.