On the depth r Bernstein projector
In this paper we prove an explicit formula for the Bernstein projector to representations of depth ≤ 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 representati...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
Springer International Publishing
2019
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| Online Access: | http://hdl.handle.net/1721.1/120924 https://orcid.org/0000-0001-5902-8989 |
| Summary: | In this paper we prove an explicit formula for the Bernstein projector to representations of depth ≤ 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. |
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