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Regular Bernstein blocks

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journal contribution
posted on 2023-08-05, 13:05 authored by Jeffrey AdlerJeffrey Adler, Manish Mishra

For a connected reductive group G defined over a non-archimedean local field F, we consider the Bernstein blocks in the category of smooth representations of G(F). Bernstein blocks whose cuspidal support involves a regular supercuspidal representation are called regular Bernstein blocks. Most Bernstein blocks are regular when the residual characteristic of F is not too small. Under mild hypotheses on the residual characteristic, we show that the Bernstein center of a regular Bernstein block of G(F) is isomorphic to the Bernstein center of a regular depth-zero Bernstein block ofG0(F), where G0 is a certain twisted Levi subgroup of G. In some cases, we show that the blocks themselves are equivalent, and as a consequence we prove the ABPS Conjecture in some new cases.



Journal fur die Reine und Angewandte Mathematik


Published ahead of print.


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