A CATEGORICAL APPROACH TO THE STABLE CENTER CONJECTURE

作者：Bezrukavnikov Roman^*; Kazhdan David; Varshavsky Yakov

来源：Asterisque, 2015, (369): 27-97.

• Local Langlands conjecture
• Bernstein center
• affine Weyl group
• categorical Hecke algebra
• infinity categories
• l-adic sheaves

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.

• 出版日期2015