{"id":{"repo_id":"freiburg-diss","oai_identifier":"oai:freidok.uni-freiburg.de:67"},"canonical_url":"https://search.dev.ndltd.org/etd/freiburg-diss/oai:freidok.uni-freiburg.de:67","repository":{"repo_id":"freiburg-diss","name":"University of Freiburg","base_url":"https://freidok.uni-freiburg.de/oai/oai2.php"},"display":{"title":"The fine structure of translation functors, the triangle function and a construction of R-matrices","abstract":"Let E be a simple finite-dimensional representation of a semisimple Lie algebra <br>with extremal weight <br>u and let e in E_{ <br>u} nonzero. <br>Let M( au) be the Verma module with highest weight au and v_{ au} the canonical <br>generator. <br>We investigate the projection of e otimes v_{ au} in E otimes M( au) on the <br>central character chi( au + <br>u). This is a rational function in au and we <br>calculate its poles and zeros. <br>We then apply this result in order to compare translation functors. <br>We also describe a transformation for quantum dynamical R-matrices.","abstract_html":"Let E be a simple finite-dimensional representation of a semisimple Lie algebra &lt;br&gt;with extremal weight &lt;br&gt;u and let e in E_{ &lt;br&gt;u} nonzero. &lt;br&gt;Let M( au) be the Verma module with highest weight au and v_{ au} the canonical &lt;br&gt;generator. &lt;br&gt;We investigate the projection of e otimes v_{ au} in E otimes M( au) on the &lt;br&gt;central character chi( au + &lt;br&gt;u). This is a rational function in au and we &lt;br&gt;calculate its poles and zeros. &lt;br&gt;We then apply this result in order to compare translation functors. &lt;br&gt;We also describe a transformation for quantum dynamical R-matrices.","abstract_has_math":false,"creators":["Günzl, Karen"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":["Soergel, Wolfgang"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":null,"date_issued":"","date_published":null,"updated_at":"2026-07-24T02:21:24Z","subjects":["Kategorie O","Verschiebungsfunktoren","Dreiecksfunktion","quantendynamische Yang-Baxter-Gleichung","representation theory","Lie algebra","translation functor","Verma module","R-matrix"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://freidok.uni-freiburg.de/data/67","outbound_label":"Repository record","outbound_source":"source_url"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Soergel, Wolfgang"]},{"key":"dc:creator","label":"Author","values":["Günzl, Karen"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:type","label":"Dc Type","values":["DoctoralThesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Kategorie O","Verschiebungsfunktoren","Dreiecksfunktion","quantendynamische Yang-Baxter-Gleichung","representation theory","Lie algebra","translation functor","Verma module","R-matrix"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Let E be a simple finite-dimensional representation of a semisimple Lie algebra <br>with extremal weight <br>u and let e in E_{ <br>u} nonzero. <br>Let M( au) be the Verma module with highest weight au and v_{ au} the canonical <br>generator. <br>We investigate the projection of e otimes v_{ au} in E otimes M( au) on the <br>central character chi( au + <br>u). This is a rational function in au and we <br>calculate its poles and zeros. <br>We then apply this result in order to compare translation functors. <br>We also describe a transformation for quantum dynamical R-matrices."]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["The fine structure of translation functors, the triangle function and a construction of R-matrices"]}]}],"canonical_facts":{"dc:contributor":["Soergel, Wolfgang"],"dc:creator":["Günzl, Karen"],"dc:description.abstract":["Let E be a simple finite-dimensional representation of a semisimple Lie algebra <br>with extremal weight <br>u and let e in E_{ <br>u} nonzero. <br>Let M( au) be the Verma module with highest weight au and v_{ au} the canonical <br>generator. <br>We investigate the projection of e otimes v_{ au} in E otimes M( au) on the <br>central character chi( au + <br>u). This is a rational function in au and we <br>calculate its poles and zeros. <br>We then apply this result in order to compare translation functors. <br>We also describe a transformation for quantum dynamical R-matrices."],"dc:format.medium":["application/pdf"],"dc:subject":["Kategorie O","Verschiebungsfunktoren","Dreiecksfunktion","quantendynamische Yang-Baxter-Gleichung","representation theory","Lie algebra","translation functor","Verma module","R-matrix"],"dc:title":["The fine structure of translation functors, the triangle function and a construction of R-matrices"],"dc:type":["DoctoralThesis"]},"updated_at":"2026-07-24T02:21:24Z"}