{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/99307"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/99307","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"Spherical Elements in the Affine Yokonuma-Hecke Algebra","abstract":"In Chapter 1 we introduce the Yokonuma-Hecke Algebra and a Yokonuma-Hecke Algebra-module. In Chapter 2 we determine that the possible eigenvalues of particular elements in the Yokonuma-Hecke Algebra acting on the module. In Chapter 3 we find determine module subspaces and eigenspaces that are isomorphic. In Chapter 4 we determine the structure of the q-eigenspace. In Chapter 5 we determine the spherical elements of the module.","abstract_html":"In Chapter 1 we introduce the Yokonuma-Hecke Algebra and a Yokonuma-Hecke Algebra-module. In Chapter 2 we determine that the possible eigenvalues of particular elements in the Yokonuma-Hecke Algebra acting on the module. In Chapter 3 we find determine module subspaces and eigenspaces that are isomorphic. In Chapter 4 we determine the structure of the q-eigenspace. In Chapter 5 we determine the spherical elements of the module.","abstract_has_math":false,"creators":["Shaplin, Richard Martin III"],"institution":"Virginia Tech","degree_name":"Master of Science","degree_level":"masters","degree_discipline":"Mathematics","degree_department":"Mathematics","school":null,"contributors":[],"advisors":[],"committee_chairs":["Orr, Daniel D."],"committee_members":["Linnell, Peter A.","Shimozono, Mark M."],"year":2020,"date_issued":"2020-07-08","date_published":"2020-07-08","updated_at":"2026-07-22T22:19:29Z","subjects":["Affine Yokonuma–Hecke Algebras","Spherical Elements"],"languages":[],"rights":["In Copyright"],"rights_urls":["http://rightsstatements.org/vocab/InC/1.0/"],"identifier_entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["vt_gsexam:26025"],"render_values":[{"text":"vt_gsexam:26025","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/10919/99307","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.committeechair","label":"Committee Chair","values":["Orr, Daniel D."]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Linnell, Peter A.","Shimozono, Mark M."]},{"key":"dc:contributor.department","label":"Department","values":["Mathematics"]},{"key":"dc:creator","label":"Author","values":["Shaplin, Richard Martin III"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2020-07-09T08:01:11Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2020-07-09T08:01:11Z"]},{"key":"dc:date.issued","label":"Date","values":["2020-07-08"]},{"key":"dc:publisher","label":"Institution","values":["Virginia Tech"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["masters"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Virginia Polytechnic Institute and State University"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Affine Yokonuma–Hecke Algebras","Spherical Elements"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["In Copyright"]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://rightsstatements.org/vocab/InC/1.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["vt_gsexam:26025"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10919/99307"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["In Chapter 1 we introduce the Yokonuma-Hecke Algebra and a Yokonuma-Hecke Algebra-module. In Chapter 2 we determine that the possible eigenvalues of particular elements in the Yokonuma-Hecke Algebra acting on the module. In Chapter 3 we find determine module subspaces and eigenspaces that are isomorphic. In Chapter 4 we determine the structure of the q-eigenspace. In Chapter 5 we determine the spherical elements of the module."]},{"key":"dc:description.abstractgeneral","label":"General Abstract","values":["The Yokonuma-Hecke Algebra-module is a vector space over a particular field. Acting on vectors from the module by any element of the Yokonuma-Hecke Algebra corresponds to a linear transformation. Then, for each element we can find eigenvalues and eigenvectors. The transformations that we are considering all have the same eigenvalues. So, we consider the intersection of all the eigenspaces that correspond to the same eigenvalue. I.e. vectors that are eigenvectors of all of the elements. We find an algorithm that generates a basis for said vectors."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Master of Science"]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["ETD"]},{"key":"dc:title","label":"Title","values":["Spherical Elements in the Affine Yokonuma-Hecke Algebra"]}]}],"canonical_facts":{"dc:contributor.committeechair":["Orr, Daniel D."],"dc:contributor.committeemember":["Linnell, Peter A.","Shimozono, Mark M."],"dc:contributor.department":["Mathematics"],"dc:creator":["Shaplin, Richard Martin III"],"dc:date.accessioned":["2020-07-09T08:01:11Z"],"dc:date.available":["2020-07-09T08:01:11Z"],"dc:date.issued":["2020-07-08"],"dc:description.abstract":["In Chapter 1 we introduce the Yokonuma-Hecke Algebra and a Yokonuma-Hecke Algebra-module. In Chapter 2 we determine that the possible eigenvalues of particular elements in the Yokonuma-Hecke Algebra acting on the module. In Chapter 3 we find determine module subspaces and eigenspaces that are isomorphic. In Chapter 4 we determine the structure of the q-eigenspace. In Chapter 5 we determine the spherical elements of the module."],"dc:description.abstractgeneral":["The Yokonuma-Hecke Algebra-module is a vector space over a particular field. Acting on vectors from the module by any element of the Yokonuma-Hecke Algebra corresponds to a linear transformation. Then, for each element we can find eigenvalues and eigenvectors. The transformations that we are considering all have the same eigenvalues. So, we consider the intersection of all the eigenspaces that correspond to the same eigenvalue. I.e. vectors that are eigenvectors of all of the elements. We find an algorithm that generates a basis for said vectors."],"dc:description.degree":["Master of Science"],"dc:format.medium":["ETD"],"dc:identifier.other":["vt_gsexam:26025"],"dc:identifier.uri":["http://hdl.handle.net/10919/99307"],"dc:publisher":["Virginia Tech"],"dc:rights":["In Copyright"],"dc:rights.uri":["http://rightsstatements.org/vocab/InC/1.0/"],"dc:subject":["Affine Yokonuma–Hecke Algebras","Spherical Elements"],"dc:title":["Spherical Elements in the Affine Yokonuma-Hecke Algebra"],"dc:type":["Thesis"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["masters"],"thesis:degree_name":["Master of Science"],"thesis:institution_name":["Virginia Polytechnic Institute and State University"]},"updated_at":"2026-07-22T22:19:29Z"}