A survey paper in
the current Bulletin
of the
American Mathematical Society (Vol. 45, No. 1, January 2008, pp.
1-60) is titled "
Reflection
Groups in
Algebraic Geometry." That paper deals with groups defined
over
fields of characteristic zero; this note is to point out some
references for reflection groups over fields of positive
characteristic.
Recall that a reflection group may be defined as a group of linear
transformations of a vector space over a (possibly finite) field that
is generated by reflections-- transformations that fix a hyperplane
pointwise.
Characteristic Two:
For characteristic two, there exist easily visualized reflection
groups acting on the 2x2 square, the 2x2x2 cube, the 4x4 square, and
the 4x4x4 cube. For details, see
Binary
Coordinate Systems and
Finite Geometry of
the Square and Cube.