{"id":{"repo_id":"byu","oai_identifier":"oai:scholarsarchive.byu.edu:etd-1529"},"canonical_url":"https://search.dev.ndltd.org/etd/byu/oai:scholarsarchive.byu.edu:etd-1529","repository":{"repo_id":"byu","name":"Brigham Young University","base_url":"https://scholarsarchive.byu.edu/do/oai/"},"display":{"title":"Matrix Representations of Automorphism Groups of Free Groups","abstract":"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.","abstract_html":"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.","abstract_has_math":false,"creators":["Andrus, Ivan B."],"institution":"Brigham Young University - Provo","degree_name":"MS","degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":null,"date_issued":"","date_published":null,"updated_at":"2026-07-24T01:28:03Z","subjects":["representation","automorphism group","free group","automorphism group of free group","hyperoctahedral group","young diagram","Mathematics"],"languages":["English"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://scholarsarchive.byu.edu/etd/530","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Andrus, Ivan B."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2005-06-20T07:00:00Z"]},{"key":"dc:publisher","label":"Institution","values":["Brigham Young University - Provo"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["MS"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["representation","automorphism group","free group","automorphism group of free group","hyperoctahedral group","young diagram","Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["English"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholarsarchive.byu.edu/etd/530","https://scholarsarchive.byu.edu/context/etd/article/1529/viewcontent/ETD_CISOPTR_350.pdf"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Physical and Mathematical Sciences; Mathematics"]},{"key":"dc:description.abstract","label":"Abstract","values":["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."]},{"key":"dc:format","label":"Dc Format","values":["application:pdf"]},{"key":"dc:source","label":"Dc Source","values":["Brigham Young University - Provo"]},{"key":"dc:title","label":"Title","values":["Matrix Representations of Automorphism Groups of Free Groups"]}]}],"canonical_facts":{"dc:creator":["Andrus, Ivan B."],"dc:date":["2005-06-20T07:00:00Z"],"dc:description":["Physical and Mathematical Sciences; Mathematics"],"dc:description.abstract":["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."],"dc:format":["application:pdf"],"dc:identifier":["https://scholarsarchive.byu.edu/etd/530","https://scholarsarchive.byu.edu/context/etd/article/1529/viewcontent/ETD_CISOPTR_350.pdf"],"dc:language":["English"],"dc:publisher":["Brigham Young University - Provo"],"dc:source":["Brigham Young University - Provo"],"dc:subject":["representation","automorphism group","free group","automorphism group of free group","hyperoctahedral group","young diagram","Mathematics"],"dc:title":["Matrix Representations of Automorphism Groups of Free Groups"],"dc:type":["Thesis"],"thesis:degree_name":["MS"]},"updated_at":"2026-07-24T01:28:03Z"}