Unramified affine Springer fibers and isospectral Hilbert schemes

• Oscar Kivinen ^[1]
  1. [1] California Institute of Technology

     California Institute of Technology

     Estados Unidos

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 26, Nº. 4, 2020
• Idioma: inglés
• DOI: 10.1007/s00029-020-00587-1
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• Resumen

  • For any connected reductive group G over C, we revisit Goresky–Kottwitz–MacPherson’s description of the torus equivariant Borel–Moore homology of affine Springer fibers Spγ⊂GrG, where γ=ztd and z is a regular semisimple element in the Lie algebra of G. In the case G=GLn, we relate the equivariant cohomology of Spγ to Haiman’s work on the isospectral Hilbert scheme of points on the plane. We also explain the connection to the HOMFLY homology of (n, dn)-torus links, and formulate a conjecture describing the homology of the Hilbert scheme of points on the curve {xn=ydn}.