An Euler-Poincaré formula for depth zero Bernstein projector

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 the projector to an individual depth zero Bernstein component in terms of an equivariant system of Peter--Weyl idempotents of parahoric subgroups P associated to a block of the reductive quotient of P.

38 pages, 2 figures