An Euler-Poincaré formula for a depth zero Bernstein projector

Barbasch, Dan; Ciubotaru, Dan; Moy, Allen

doi:10.1090/ert/525

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 $\mathscr {G}_{F}/\mathscr {G}^{+}_{F}$.

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