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TOWARD A MACKEY FORMULA FOR COMPACT RESTRICTION OF CHARACTER SHEAVES
 

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 Mackey-type 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 Mackey-type 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 non-Archimendean 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

  

Source: Achar, Pramod - Department of Mathematics, Louisiana State University

 

Collections: Mathematics