Seminar in Representation Theory
Reduction to depth-zero for tame $p$-adic groups and generic representations
2026/08/05 (Wed.) 10:00~11:30
- Date : 2026/08/05 (Wed.) 10:00~11:30
- Location : Seminar Room 638, Institute of Mathematics (NTU Campus)
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Speaker : Kazuma Ohara (Max Planck Institute for Mathematics)
- Organizer : Cheng-Chiang Tsai (AS)
- Abstract :
The category of smooth complex representations of a $p$-adic group decomposes into a product of indecomposable full subcategories, called Bernstein blocks. In joint work with Jeffrey D. Adler, Jessica Fintzen, and Manish Mishra, we proved, under explicit tameness assumptions, that every Bernstein block is equivalent to a special kind of Bernstein block, called a depth-zero block. Such blocks are closely related to representations of finite groups of Lie type and are therefore much more accessible than general Bernstein blocks.
However, the resulting “reduction-to-depth-zero” functor is not unique. In this talk, I will explain the result that the functor can be chosen to preserve the generic representations in each block, which play an important role in the local Langlands correspondence. I will also explain that this requirement determines the functor “outside the supercuspidal part”.
The talk is based on joint work in progress with Cheng-Chiang Tsai.
