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

Source: Aubert, Anne-Marie - Institut de Mathématiques de Jussieu

Collections: Mathematics