Motivic zeta functions of infinite-dimensional Lie algebras

• Marcus du Sautoy ^[2] ; François Loeser ^[1]
  1. [1] École Normale Supérieure

     École Normale Supérieure

     Francia

     
  2. [2] Mathematical Institute, Oxford, U.K.
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 10, Nº. 2, 2004, págs. 253-303
• Idioma: inglés
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• Resumen

  • The paper shows how to associate a motivic zeta function with a large class of infinite dimensional Lie algebras. These include loop algebras, affine Kac-Moody algebras, the Virasoro algebra and Lie algebras of Cartan type. The concept of a motivic zeta functions provides a good language to talk about the uniformity in p of local p-adic zeta functions of finite dimensional Lie algebras. The theory of motivic integration is employed to prove the rationality of motivic zeta functions associated to certain classes of infinite dimensional Lie algebras.