
School of Mathematics and Statistics
Anthony Henderson
University of Sydney
Spherical functions and character sheaves
Friday August 31st, 121pm,
Carslaw 375.
Let G(F_{q}) be a finite reductive group and
H(F_{q}) the subgroup of fixed points of some
involution. The set of cosets
G(F_{q})/H(F_{q}) is called a
finite symmetric space The spherical functions on this
space are the averages, over these cosets, of the irreducible
characters of G(F_{q}). Computing the values
of these spherical functions is a generalization of the muchstudied
problem of computing the character table of finite reductive groups.
To solve the latter problem, Lusztig introduced the notion of
character sheaves on groups. In this talk I will explain how the more
general character sheaves on symmetric spaces (in the sense of
Ginzburg and Grojnowski) help in the former problem, and examine some
special cases where they lead to a solution.
