 
Summary: TOWARD A MACKEY FORMULA FOR COMPACT
RESTRICTION OF CHARACTER SHEAVES
PRAMOD N. ACHAR AND CLIFTON L.R. CUNNINGHAM
Abstract. We generalize [6, Theorem 3] to a Mackeytype formula for the
compact restriction of a semisimple perverse sheaf produced by parabolic in
duction from a character sheaf, under certain conditions on the parahoric group
scheme used to define compact restriction. This provides new tools for match
ing character sheaves with admissible representations.
Introduction
In this paper we prove a Mackeytype formula for the compact restriction func
tors introduced in [6]. The main result, Theorem 1, applies to any connected
reductive linear algebraic group G over any nonArchimendean local field K that
satisfies the following three hypotheses:
(H.0) G is the generic fibre of a smooth, connected reductive group scheme over
the ring of integers OK of K;
(H.1) the characteristic of K is not 2 (in particular, this condition is met if the
characteristic of K is 0);
(H.2) for every parabolic subgroup P¯K G ×Spec(K) Spec ¯K there is a finite
unramified extension K of K and a subgroup P G ×Spec(K) Spec (K )
such that P ×Spec(K ) Spec ¯K is conjugate to P¯K by an element of G(Ktr
