{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/49392"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/49392","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"On semi-invariants of filtered representations of quivers and the cotangent bundle of the enhanced Grothendieck-Springer resolution","abstract":"We introduce the notion of filtered representations of quivers, which is related to usual quiver representations, but is a systematic generalization of conjugacy classes of $n\\times n$ matrices to (block) upper triangular matrices up to conjugation by invertible (block) upper triangular matrices. With this notion in mind, we describe the ring of invariant polynomials for interesting families of quivers, namely, finite $ADE$-Dynkin quivers and affine type $\\widetilde{A}$-Dynkin quivers. We then study their relation to an important and fundamental object in representation theory called the Grothendieck-Springer resolution, and we conclude by stating several conjectures, suggesting further research.","abstract_html":"We introduce the notion of filtered representations of quivers, which is related to usual quiver representations, but is a systematic generalization of conjugacy classes of $n\\times n$ matrices to (block) upper triangular matrices up to conjugation by invertible (block) upper triangular matrices. With this notion in mind, we describe the ring of invariant polynomials for interesting families of quivers, namely, finite $ADE$-Dynkin quivers and affine type $\\widetilde{A}$-Dynkin quivers. We then study their relation to an important and fundamental object in representation theory called the Grothendieck-Springer resolution, and we conclude by stating several conjectures, suggesting further research.","abstract_has_math":true,"creators":["Im, Mee Seong"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Schenck, Henry K.","Nevins, Thomas A.","Kedem, Rinat","Bergvelt, Maarten J."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014-05-30T16:41:46Z","date_published":"2014-05-30T16:41:46Z","updated_at":"2026-07-22T22:25:38Z","subjects":["Algebraic geometry","representation theory","quiver varieties","filtered quiver variety","quiver flag variety","semi-invariant polynomials","invariant subring","Derksen-Weyman","Domokos-Zubkov","Schofield-van den Bergh","ADE-Dynkin quivers","affine Dynkin quivers","quivers with at most two pathways between any two vertices","filtration of vector spaces","classical invariant theory","the Hamiltonian reduction of the cotangent bundle of the enhanced Grothendieck-Springer resolution","almost-commuting varieties","affine quotient"],"languages":["en"],"rights":["Copyright 2014 Mee Seong Im"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/49392","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Schenck, Henry K.","Nevins, Thomas A.","Kedem, Rinat","Bergvelt, Maarten J."]},{"key":"dc:creator","label":"Author","values":["Im, Mee Seong"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2014-05-30T16:41:46Z","2014-05"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Algebraic geometry","representation theory","quiver varieties","filtered quiver variety","quiver flag variety","semi-invariant polynomials","invariant subring","Derksen-Weyman","Domokos-Zubkov","Schofield-van den Bergh","ADE-Dynkin quivers","affine Dynkin quivers","quivers with at most two pathways between any two vertices","filtration of vector spaces","classical invariant theory","the Hamiltonian reduction of the cotangent bundle of the enhanced Grothendieck-Springer resolution","almost-commuting varieties","affine quotient"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2014 Mee Seong Im"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/49392"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["We introduce the notion of filtered representations of quivers, which is related to usual quiver representations, but is a systematic generalization of conjugacy classes of $n\\times n$ matrices to (block) upper triangular matrices up to conjugation by invertible (block) upper triangular matrices. With this notion in mind, we describe the ring of invariant polynomials for interesting families of quivers, namely, finite $ADE$-Dynkin quivers and affine type $\\widetilde{A}$-Dynkin quivers. We then study their relation to an important and fundamental object in representation theory called the Grothendieck-Springer resolution, and we conclude by stating several conjectures, suggesting further research.","Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2014-04-18T13:41:19Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 1 Im_MeeSeong.pdf: 1112913 bytes, checksum: 8bc94888423425498f92f49e5709a1ce (MD5)","Made available in DSpace on 2014-05-30T16:41:46Z (GMT). No. of bitstreams: 2 Mee Seong_Im.pdf: 1112913 bytes, checksum: 8bc94888423425498f92f49e5709a1ce (MD5) license.txt: 4058 bytes, checksum: ef56fdb200ab46b3d2d21b5b5e0b8eeb (MD5)"]},{"key":"dc:title","label":"Title","values":["On semi-invariants of filtered representations of quivers and the cotangent bundle of the enhanced Grothendieck-Springer resolution"]}]}],"canonical_facts":{"dc:contributor":["Schenck, Henry K.","Nevins, Thomas A.","Kedem, Rinat","Bergvelt, Maarten J."],"dc:creator":["Im, Mee Seong"],"dc:date":["2014-05-30T16:41:46Z","2014-05"],"dc:description":["We introduce the notion of filtered representations of quivers, which is related to usual quiver representations, but is a systematic generalization of conjugacy classes of $n\\times n$ matrices to (block) upper triangular matrices up to conjugation by invertible (block) upper triangular matrices. With this notion in mind, we describe the ring of invariant polynomials for interesting families of quivers, namely, finite $ADE$-Dynkin quivers and affine type $\\widetilde{A}$-Dynkin quivers. We then study their relation to an important and fundamental object in representation theory called the Grothendieck-Springer resolution, and we conclude by stating several conjectures, suggesting further research.","Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2014-04-18T13:41:19Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 1 Im_MeeSeong.pdf: 1112913 bytes, checksum: 8bc94888423425498f92f49e5709a1ce (MD5)","Made available in DSpace on 2014-05-30T16:41:46Z (GMT). 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