A categorical approach to the stable center conjecture

Roman Bezrukavnikov, David Kazhdan, Yakov Varshavsky

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


Let G be a connected reductive group over a local non-archimedean field F. The stable center conjecture provides an intrinsic decomposition of the set of equivalence classes of smooth irreducible representations of G(F), which is only slightly coarser than the conjectural decomposition into L-packets. In this work we propose a way to verify this conjecture for depth zero representations. As an illustration of our method, we show that the Bernstein projector to the depth zero spectrum is stable.

Original languageAmerican English
Pages (from-to)27-97
Number of pages71
Issue number369
StatePublished - 2015

Bibliographical note

Publisher Copyright:
© Astérisque 369, SMF 2015.


  • Affine Weyl group
  • Bernstein center
  • Categorical Hecke algebra
  • Infinity categories
  • L-adic sheaves
  • Local Langlands conjecture


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