On the depth r Bernstein projector
Roman Bezrukavnikov, David Kazhdan, Yakov Varshavsky

TL;DR
This paper provides an explicit formula for the Bernstein projector for representations of a given depth, revealing its support, stability, and relation to the Steinberg character, with local proofs for integral depths.
Contribution
It introduces a new explicit formula for the Bernstein projector of depth r and demonstrates its support, stability, and connection to the Steinberg representation.
Findings
Depth zero projector supported on topologically unipotent elements
Depth zero projector equals Steinberg character restriction
Depth r projector is stable
Abstract
In this paper we prove an explicit formula for the Bernstein projector to representations of depth at most 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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
