  In this article we study the perverse sheaf on Drinfeld's compactification
obtained by applying the geometric Jacquet functor (alias nearby cycles) to a
nondegenerate Whittaker sheaf. Namely, we describe its restrictions along the
defect stratification in terms of the Langlands dual Lie algebra, in particular
showing that this nearby cycles sheaf is tilting. We also describe the
subquotients of the monodromy filtration using the Picard-Lefschetz oscillators
introduced by S. Schieder, including a proof that the subquotients are
semisimple without reference to any theory of weights. This argument instead
relies on the action of the Langlands dual Lie algebra on compactified
Eisenstein series (or what is essentially the same, cohomology of quasimaps
into the flag variety) constructed by Feigin, Finkelberg, Kuznetsov, and
Mirkovic.

Algebraic Geometry;Representation Theory