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An Euler-Poincaré formula for a depth zero Bernstein projector

Authors: Dan Barbasch, Dan Ciubotaru and Allen Moy
Journal: Represent. Theory 23 (2019), 154-187
MSC (2010): Primary 22E50, 22E35
Published electronically: March 28, 2019
MathSciNet review: 3932569
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Abstract | References | Similar Articles | Additional Information


Work of Bezrukavnikov-Kazhdan-Varshavsky uses an equivariant system of trivial idempotents of Moy-Prasad groups to obtain an Euler-Poincaré formula for the r-depth Bernstein projector. We establish an Euler-Poincaré formula for natural sums of depth zero Bernstein projectors (which is often the projector of a single Bernstein component) in terms of an equivariant system of Peter-Weyl idempotents of parahoric subgroups $ \mathscr {G}_{F}$ associated to a block of the reductive quotient $ \mathscr {G}_{F}/\mathscr {G}^{+}_{F}$.

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Additional Information

Dan Barbasch
Affiliation: Department of Mathematics, Malott Hall, Cornell University, Ithaca, New York 14853–0099

Dan Ciubotaru
Affiliation: Mathematical Institute, Andrew Wiles Building, University of Oxford, Oxford, OX2 6GG, United Kingdom

Allen Moy
Affiliation: Department of Mathematics, The Hong Kong University of Science and Technology, Clear Water Bay Road, Hong Kong

Keywords: Bernstein center, Bernstein projector, Bruhat--Tits building, depth, distribution, equivariant system, essentially compact, Euler--Poincar{\'e}, idempotent, resolution
Received by editor(s): March 10, 2018
Received by editor(s) in revised form: February 14, 2019
Published electronically: March 28, 2019
Additional Notes: The first author was partly supported by NSA grant H98230-16-1-0006.
The second author was partly supported by United Kingdom EPSRC grant EP/N033922/1.
The third author was partly supported by Hong Kong Research Grants Council grant CERG #603813.
Article copyright: © Copyright 2019 American Mathematical Society