Algebraic Group - Coxeter Groups

Coxeter Groups

There are a number of analogous results between algebraic groups and Coxeter groups – for instance, the number of elements of the symmetric group is, and the number of elements of the general linear group over a finite field is the q-factorial ; thus the symmetric group behaves as though it were a linear group over "the field with one element". This is formalized by the field with one element, which considers Coxeter groups to be simple algebraic groups over the field with one element.