On the depth r Bernstein projector

Roman Bezrukavnikov ^[1] ; David Kazhdan ^[2] ; Yakov Varshavsky ^[2]
1. [1] Massachusetts Institute of Technology
  
  Massachusetts Institute of Technology
  
  City of Cambridge, Estados Unidos
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. 2271-2311
Idioma: inglés
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Resumen
- In this paper we prove an explicit formula for the Bernstein projector to representations of depth ≤r . As a consequence, we show that the depth zero Bernstein projector is supported on topologically unipotent elements and it is equal to the restriction of the character of the Steinberg representation. As another application, we deduce that the depth r Bernstein projector is stable. Moreover, for integral depths our proof is purely local.