Cyclic sieving, rotation, and geometric representation theory

• Bruce Fontaine ^[1] ; Joel Kamnitzer ^[2]
  1. [1] Cornell University

     Cornell University

     City of Ithaca, Estados Unidos

     
  2. [2] University of Toronto

     University of Toronto

     Canadá

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 20, Nº. 2, 2014, págs. 609-625
• Idioma: inglés
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• Resumen

  • We study rotation of invariant vectors in tensor products of minuscule representations. We define a combinatorial notion of rotation of minuscule Littelmann paths. Using affine Grassmannians, we show that this rotation action is realized geometrically as rotation of components of the Satake fiber. As a consequence, we have a basis for invariant spaces, which is permuted by rotation (up to global sign). Finally, we diagonalize the rotation operator by showing that its eigenspaces are given by intersection homology of quiver varieties. As a consequence, we generalize Rhoades’ work on the cyclic sieving phenomenon.