{"id":{"repo_id":"aachen","oai_identifier":"oai:publications.rwth-aachen.de:58877"},"canonical_url":"https://search.dev.ndltd.org/etd/aachen/oai:publications.rwth-aachen.de:58877","repository":{"repo_id":"aachen","name":"RWTH Aachen University","base_url":"https://publications.rwth-aachen.de/oai2d"},"display":{"title":"Untersuchungen zu James' Vermutung über Iwahori-Hecke-Algebren vom Typ A","abstract":"This thesis deals with a conjecture by Gordon James from 1990 and a variant by Meinolf Geck about decomposition maps of the generic Iwahori-Hecke algebra H of the symmetric group on n points arising from specialization to characteristic l>0. If the parameter of the algebra is specialized to an element q of GF(l) with multiplicative order e, the conjecture states, that, for el>n, the decomposition map does not depend on l and q, but only on e. The main result of the present work is the following reformulation of the James-Geck conjecture: For el>n every primitive idempotent in the extension of scalars AH is primitive as idempotent in the algebra A'H, where A and A' are rings of characteristic 0 (which are explicitly constructed for l and q), such that A is contained in A' and therefore AH in A'H. Thus an equivalent statement is given, which contains only rings and algebras of characteristic 0. To prove equivalence, generalizations of the well-known methods of lifting of idempotents and of Brauer reciprocity are developed. In addition results and observations are presented, that might lead to an approach to a proof of the above mentioned reformulation. A method is presented, how one can derive explicit formulae for primitive idempotents in non-semi-simple symmetric algebras using matrix representations on projective indecomposable modules. Such matrix representations seem to arise naturally from the Kazhdan-Lusztig cell modules. Another possible attack for a proof stems from another result of the present thesis, an explicit construction of a Wedderburn decomposition for H using the Kazhdan-Lusztig basis.","abstract_html":"This thesis deals with a conjecture by Gordon James from 1990 and a variant by Meinolf Geck about decomposition maps of the generic Iwahori-Hecke algebra H of the symmetric group on n points arising from specialization to characteristic l>0. If the parameter of the algebra is specialized to an element q of GF(l) with multiplicative order e, the conjecture states, that, for el>n, the decomposition map does not depend on l and q, but only on e. The main result of the present work is the following reformulation of the James-Geck conjecture: For el>n every primitive idempotent in the extension of scalars AH is primitive as idempotent in the algebra A'H, where A and A' are rings of characteristic 0 (which are explicitly constructed for l and q), such that A is contained in A' and therefore AH in A'H. Thus an equivalent statement is given, which contains only rings and algebras of characteristic 0. To prove equivalence, generalizations of the well-known methods of lifting of idempotents and of Brauer reciprocity are developed. In addition results and observations are presented, that might lead to an approach to a proof of the above mentioned reformulation. A method is presented, how one can derive explicit formulae for primitive idempotents in non-semi-simple symmetric algebras using matrix representations on projective indecomposable modules. Such matrix representations seem to arise naturally from the Kazhdan-Lusztig cell modules. Another possible attack for a proof stems from another result of the present thesis, an explicit construction of a Wedderburn decomposition for H using the Kazhdan-Lusztig basis.","abstract_has_math":false,"creators":["Neunhöffer, Max"],"institution":"Publikationsserver der RWTH Aachen University","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":["Hiß, Gerhard"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2003,"date_issued":"2003","date_published":"2003","updated_at":"2026-07-30T19:42:31Z","subjects":["info:eu-repo/classification/ddc/510","Mathematik","Iwahori Hecke","Algebra","James Conjecture","Kazhdan Lusztig","Cell Module Type A"],"languages":["ger"],"rights":["info:eu-repo/semantics/openAccess"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["https://publications.rwth-aachen.de/search?p=id:%22RWTH-CONV-120704%22"],"render_values":[{"text":"https://publications.rwth-aachen.de/search?p=id:%22RWTH-CONV-120704%22","href":"https://publications.rwth-aachen.de/search?p=id:%22RWTH-CONV-120704%22","code":true}]}]},"links":{"outbound_url":"https://publications.rwth-aachen.de/record/58877","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Hiß, Gerhard"]},{"key":"dc:creator","label":"Author","values":["Neunhöffer, Max"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:coverage","label":"Dc Coverage","values":["DE"]},{"key":"dc:date","label":"Dc Date","values":["2003"]},{"key":"dc:publisher","label":"Institution","values":["Publikationsserver der RWTH Aachen University"]},{"key":"dc:relation","label":"Dc Relation","values":["info:eu-repo/semantics/altIdentifier/urn/urn:nbn:de:hbz:82-opus-5634"]},{"key":"dc:type","label":"Dc Type","values":["info:eu-repo/semantics/doctoralThesis","info:eu-repo/semantics/publishedVersion"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["info:eu-repo/classification/ddc/510","Mathematik","Iwahori Hecke","Algebra","James Conjecture","Kazhdan Lusztig","Cell Module Type A"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["ger"]},{"key":"dc:rights","label":"Dc Rights","values":["info:eu-repo/semantics/openAccess"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://publications.rwth-aachen.de/record/58877","https://publications.rwth-aachen.de/search?p=id:%22RWTH-CONV-120704%22"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["This thesis deals with a conjecture by Gordon James from 1990 and a variant by Meinolf Geck about decomposition maps of the generic Iwahori-Hecke algebra H of the symmetric group on n points arising from specialization to characteristic l>0. If the parameter of the algebra is specialized to an element q of GF(l) with multiplicative order e, the conjecture states, that, for el>n, the decomposition map does not depend on l and q, but only on e. The main result of the present work is the following reformulation of the James-Geck conjecture: For el>n every primitive idempotent in the extension of scalars AH is primitive as idempotent in the algebra A'H, where A and A' are rings of characteristic 0 (which are explicitly constructed for l and q), such that A is contained in A' and therefore AH in A'H. Thus an equivalent statement is given, which contains only rings and algebras of characteristic 0. To prove equivalence, generalizations of the well-known methods of lifting of idempotents and of Brauer reciprocity are developed. In addition results and observations are presented, that might lead to an approach to a proof of the above mentioned reformulation. A method is presented, how one can derive explicit formulae for primitive idempotents in non-semi-simple symmetric algebras using matrix representations on projective indecomposable modules. Such matrix representations seem to arise naturally from the Kazhdan-Lusztig cell modules. Another possible attack for a proof stems from another result of the present thesis, an explicit construction of a Wedderburn decomposition for H using the Kazhdan-Lusztig basis."]},{"key":"dc:source","label":"Dc Source","values":["Aachen : Publikationsserver der RWTH Aachen University 150 S. (2003). = Aachen, Techn. Hochsch., Diss., 2003"]},{"key":"dc:title","label":"Title","values":["Untersuchungen zu James' Vermutung über Iwahori-Hecke-Algebren vom Typ A"]}]}],"canonical_facts":{"dc:contributor":["Hiß, Gerhard"],"dc:coverage":["DE"],"dc:creator":["Neunhöffer, Max"],"dc:date":["2003"],"dc:description":["This thesis deals with a conjecture by Gordon James from 1990 and a variant by Meinolf Geck about decomposition maps of the generic Iwahori-Hecke algebra H of the symmetric group on n points arising from specialization to characteristic l>0. If the parameter of the algebra is specialized to an element q of GF(l) with multiplicative order e, the conjecture states, that, for el>n, the decomposition map does not depend on l and q, but only on e. The main result of the present work is the following reformulation of the James-Geck conjecture: For el>n every primitive idempotent in the extension of scalars AH is primitive as idempotent in the algebra A'H, where A and A' are rings of characteristic 0 (which are explicitly constructed for l and q), such that A is contained in A' and therefore AH in A'H. Thus an equivalent statement is given, which contains only rings and algebras of characteristic 0. To prove equivalence, generalizations of the well-known methods of lifting of idempotents and of Brauer reciprocity are developed. In addition results and observations are presented, that might lead to an approach to a proof of the above mentioned reformulation. A method is presented, how one can derive explicit formulae for primitive idempotents in non-semi-simple symmetric algebras using matrix representations on projective indecomposable modules. Such matrix representations seem to arise naturally from the Kazhdan-Lusztig cell modules. Another possible attack for a proof stems from another result of the present thesis, an explicit construction of a Wedderburn decomposition for H using the Kazhdan-Lusztig basis."],"dc:identifier":["https://publications.rwth-aachen.de/record/58877","https://publications.rwth-aachen.de/search?p=id:%22RWTH-CONV-120704%22"],"dc:language":["ger"],"dc:publisher":["Publikationsserver der RWTH Aachen University"],"dc:relation":["info:eu-repo/semantics/altIdentifier/urn/urn:nbn:de:hbz:82-opus-5634"],"dc:rights":["info:eu-repo/semantics/openAccess"],"dc:source":["Aachen : Publikationsserver der RWTH Aachen University 150 S. (2003). = Aachen, Techn. Hochsch., Diss., 2003"],"dc:subject":["info:eu-repo/classification/ddc/510","Mathematik","Iwahori Hecke","Algebra","James Conjecture","Kazhdan Lusztig","Cell Module Type A"],"dc:title":["Untersuchungen zu James' Vermutung über Iwahori-Hecke-Algebren vom Typ A"],"dc:type":["info:eu-repo/semantics/doctoralThesis","info:eu-repo/semantics/publishedVersion"]},"updated_at":"2026-07-30T19:42:31Z"}