Is there a version of character sheaves for non reductive algebraic groups?

Question

Lusztig's theory of character sheaves gives a geometric way to obtain character tables of finite groups of Lie type (coming from reductive groups). I am interested to know if there is a similar theory for other kinds of algebraic groups. Thanks so much.

Answer 1

Boyarchenko and Drinfeld have developed a theory of character sheaves for unipotent groups. See A motivated introduction to character sheaves and the orbit method for unipotent groups in positive characteristic for an introduction (as well as subsequent papers by Boyarchenko and Boyarchenko-Drinfeld).