-adic sheaves (Math. Ann. 292). Let j be the open immersion of
a Shimura
variety M into its Baily-Borel compactification M*. The
boundary M* - M has a natural stratification into locally closed
subsets, each of
which is itself a Shimura variety (up to taking the quotient by the
action of a finite group).
Let i be the inclusion of an individual such stratum M'.
Saito's formalism gives a functor i* j* from the bounded derived
category of Hodge
modules on M to that of Hodge modules on M'. Our result gives a
formula for the
effect of i* j* on automorphic Hodge modules, i.e., variations
of Hodge
structure coming from algebraic representations of the group associated
to M. This
formula is of a purely representation theoretical nature.