Bernstein components via the Bernstein center

• Alexander Braverman ^[1] ; David Kazhdan ^[2]
  1. [1] University of Toronto

     University of Toronto

     Canadá

     
  2. [2] Hebrew University of Jerusalem

     Hebrew University of Jerusalem

     Israel

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 22, Nº. 4 (Special Issue: The Mathematics of Joseph Bernstein), 2016, págs. 2313-2323
• Idioma: inglés
• Enlaces
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• Resumen

  • Let G be a reductive p-adic group. Let ΦΦ be an invariant distribution on G lying in the Bernstein center Z(G)Z(G) . We prove that ΦΦ is supported on compact elements in G if and only if it defines a constant function on every component of the set Irr(G)Irr(G) ; in particular, we show that the space of all elements of Z(G)Z(G) supported on compact elements is a subalgebra of Z(G)Z(G) . Our proof is a slight modification of the argument from Section 2 of Dat (J Reine Angew Math 554:69–103, 2003), where our result is proved in one direction.