Parking functions and vertex operators

• Vladimir Dotsenko ^[1]
  1. [1] Dublin Institute For Advanced Studies

     Dublin Institute For Advanced Studies

     Irlanda

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 14, Nº. 2, 2009, págs. 229-245
• Idioma: inglés
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• Resumen

  • We introduce several associative algebras and families of vector spaces associated to these algebras. Using lattice vertex operators, we obtain dimension and character formulae for these spaces. In particular, we define a family of representations of symmetric groups which turn out to be isomorphic to parking function modules. We also construct families of vector spaces whose dimensions are Catalan numbers and Fuss–Catalan numbers respectively. Conjecturally, these spaces are related to spaces of global sections of vector bundles on (zero fibres of) Hilbert schemes and representations of rational Cherednik algebras.