Higgs algebra of curves and loop crystals

Guillaume Pouchin

Research output: Working paper

Abstract

In this paper we construct geometrically some loop Kac-Moody algebras, using an analog of the construction of Kac-Moody algebras by Lusztig. In our setup, we use constructible functions on the space of Higgs Bundles on the projective line. We also use the geometry of this space to define a loop crystal, a combinatorial object analog to the crystal for Kac-Moody algebras, which contains informations about the representation theory.
Original languageEnglish
PublisherArXiv
Number of pages39
Publication statusPublished - 2010

Keywords

  • REPRESENTATION-THEORY
  • GEOMETRY
  • AFFINE LIE-ALGEBRAS

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