  In this paper we study unitary braid group representations associated with
Majorana Fermions. Majorana Fermions are represented by Majorana operators,
elements of a Clifford algebra. The paper recalls and proves a general result
about braid group representations associated with Clifford algebras, and
compares this result with the Ivanov braiding associated with Majorana
operators. The paper generalizes observations of Kauffman and Lomonaco and of
Mo-Lin Ge to show that certain strings of Majorana operators give rise to
extraspecial 2-groups and to braiding representations of the Ivanov type.
