An Euler-Poincaré formula for a depth zero Bernstein projector
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- by Dan Barbasch, Dan Ciubotaru and Allen Moy
- Represent. Theory 23 (2019), 154-187
- DOI: https://doi.org/10.1090/ert/525
- Published electronically: March 28, 2019
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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 $\mathscr {G}_{F}/\mathscr {G}^{+}_{F}$.References
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Bibliographic 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
- 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. - © Copyright 2019 American Mathematical Society
- Journal: Represent. Theory 23 (2019), 154-187
- MSC (2010): Primary 22E50, 22E35
- DOI: https://doi.org/10.1090/ert/525
- MathSciNet review: 3932569