Lifting representations of finite reductive groups: a character relation
Jeffrey D. Adler, Michael Cassel, Joshua M. Lansky, Emma Morgan, Yifei Zhao
Abstract
Given a connected reductive group
G
~
over a finite field
k
, and a semisimple
k
-automorphism
ε
of
G
~
of finite order, let
G
denote the connected part of the group of
ε
-fixed points. Then there exists a lifting from packets of representations of
G(k)
to packets for
G
~
(k)
. In the case of Deligne-Lusztig representations, we show that this lifting satisfies a character relation analogous to that of Shintani.