In this thesis, we study the representation theory of the automorphism group Aut (Fn) of a free group by studying the representation theory of three finite subgroups: two symmetric groups, Sn and Sn+1, and a Coxeter group of type Bn, also known as a hyperoctahedral group. The representation theory of these subgroups is well understood in the language of Young Diagrams, and we apply this knowledge to better understand the representation theory of Aut (Fn). We also calculate irreducible representations of Aut (Fn) in low dimensions and for small n.
College and Department
Physical and Mathematical Sciences; Mathematics
BYU ScholarsArchive Citation
Andrus, Ivan B., "Matrix Representations of Automorphism Groups of Free Groups" (2005). Theses and Dissertations. 530.
representation, automorphism group, free group, automorphism group of free group, hyperoctahedral group, young diagram