 
Summary: DEPTHZERO CHARACTER SHEAVES
ANNEMARIE AUBERT & CLIFTON CUNNINGHAM
Abstract. We introduce certain families of perverse sheaves, cal
led depthzero character sheaves, which provide a geometric frame
work for the study of characters of admissible depth zero repre
sentations of unramified padic groups which is built on Lusztig's
theory of character sheaves for groups over finite fields. To each
supercuspidal depthzero representation there corresponds a for
mal sum of depthzero character sheaves, called the model for the
representation. We associate a distribution, called a character, to
each formal sum of depthzero character sheaves and show that
the character of the model of a representation coincides with the
character of that representation on the set of regular elliptic ele
ments. The paper includes a detailed treatment of GL(n), SL(2)
and Sp(4). In the final section we indicate how to interpret depth
zero character sheaves as sheaves on a rigid analytic space.
Introduction
In their 1997 article in the Publications Math’ematiques de l'Institut
des Hautes ’
Etudes Scientifiques, Peter Schneider and Ulrich Stuhler
