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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
DOI: https://doi.org/10.1090/ert/525
Published electronically: March 28, 2019
MathSciNet review: 3932569
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Abstract: 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
MR Author ID: 30950
Email: barbasch@math.cornell.edu

Dan Ciubotaru
Affiliation: Mathematical Institute, Andrew Wiles Building, University of Oxford, Oxford, OX2 6GG, United Kingdom
MR Author ID: 754534
Email: dan.ciubotaru@maths.ox.ac.uk

Allen Moy
Affiliation: Department of Mathematics, The Hong Kong University of Science and Technology, Clear Water Bay Road, Hong Kong
MR Author ID: 127665
Email: amoy@ust.hk

Keywords: Bernstein center, Bernstein projector, Bruhat–Tits building, depth, distribution, equivariant system, essentially compact, Euler–Poincaré, 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