{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/19729"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/19729","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"The Grothendieck-Cousin complex on G/B x G/B","abstract":"In his 1978 paper, The Grothendieck-Cousin complex of an induced representation, G. Kempf computes the Cousin complex corresponding to an induced representation of a reductive algebraic group G. His technique uses the geometry of the homogeneous space G/B, B being a Borel subgroup of G. The complex gives a resolution by B-modules, which easily yields the Weyl character formula.","abstract_html":"In his 1978 paper, The Grothendieck-Cousin complex of an induced representation, G. Kempf computes the Cousin complex corresponding to an induced representation of a reductive algebraic group G. His technique uses the geometry of the homogeneous space G/B, B being a Borel subgroup of G. The complex gives a resolution by B-modules, which easily yields the Weyl character formula.","abstract_has_math":false,"creators":["LaFramboise, Thomas Louis"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Ullom, Stephen V."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-05-07T12:16:39Z","date_published":"2011-05-07T12:16:39Z","updated_at":"2026-07-22T22:25:14Z","subjects":["Mathematics"],"languages":["eng"],"rights":["Copyright 1995 LaFramboise, Thomas Louis"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI9624402","(UMI)AAI9624402"],"render_values":[{"text":"AAI9624402","href":null,"code":true},{"text":"(UMI)AAI9624402","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/19729","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Ullom, Stephen V."]},{"key":"dc:creator","label":"Author","values":["LaFramboise, Thomas Louis"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2011-05-07T12:16:39Z","10000-01-01","1995"]},{"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":["Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 1995 LaFramboise, Thomas Louis"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI9624402","(UMI)AAI9624402","http://hdl.handle.net/2142/19729"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["In his 1978 paper, The Grothendieck-Cousin complex of an induced representation, G. Kempf computes the Cousin complex corresponding to an induced representation of a reductive algebraic group G. His technique uses the geometry of the homogeneous space G/B, B being a Borel subgroup of G. The complex gives a resolution by B-modules, which easily yields the Weyl character formula.","Instead of considering G/B, we analyze the analagous situation for $G/B\\times G/B$. The Cousin complex corresponding to an induced representation in this case consists of G-modules. We are able to study the terms of the complex by exploiting parallels between the B-action on G/B and the G-action on $G/B\\times G/B$--there is a natural one-to-one correspondence between the orbits of these actions. Our work here is greatly simplified by reducing to the affine situation and applying the theory of A-G modules. We construct a spectral sequence relating the terms of the complexes. Finally, an application to the theory of D-modules is given.","Made available in DSpace on 2011-05-07T12:16:39Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9624402.pdf: 1986051 bytes, checksum: 9df74b5e3a422835a14febe4643a2b31 (MD5) Previous issue date: 1995","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T14:39:02Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:16:21-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: ETDs are only available to UIUC Users without author permission","ETDs are only available to UIUC Users without author permission","U of I Only"]},{"key":"dc:title","label":"Title","values":["The Grothendieck-Cousin complex on G/B x G/B"]}]}],"canonical_facts":{"dc:contributor":["Ullom, Stephen V."],"dc:creator":["LaFramboise, Thomas Louis"],"dc:date":["2011-05-07T12:16:39Z","10000-01-01","1995"],"dc:description":["In his 1978 paper, The Grothendieck-Cousin complex of an induced representation, G. Kempf computes the Cousin complex corresponding to an induced representation of a reductive algebraic group G. His technique uses the geometry of the homogeneous space G/B, B being a Borel subgroup of G. The complex gives a resolution by B-modules, which easily yields the Weyl character formula.","Instead of considering G/B, we analyze the analagous situation for $G/B\\times G/B$. The Cousin complex corresponding to an induced representation in this case consists of G-modules. We are able to study the terms of the complex by exploiting parallels between the B-action on G/B and the G-action on $G/B\\times G/B$--there is a natural one-to-one correspondence between the orbits of these actions. Our work here is greatly simplified by reducing to the affine situation and applying the theory of A-G modules. We construct a spectral sequence relating the terms of the complexes. Finally, an application to the theory of D-modules is given.","Made available in DSpace on 2011-05-07T12:16:39Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9624402.pdf: 1986051 bytes, checksum: 9df74b5e3a422835a14febe4643a2b31 (MD5) Previous issue date: 1995","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T14:39:02Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:16:21-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: ETDs are only available to UIUC Users without author permission","ETDs are only available to UIUC Users without author permission","U of I Only"],"dc:identifier":["AAI9624402","(UMI)AAI9624402","http://hdl.handle.net/2142/19729"],"dc:language":["eng"],"dc:rights":["Copyright 1995 LaFramboise, Thomas Louis"],"dc:subject":["Mathematics"],"dc:title":["The Grothendieck-Cousin complex on G/B x G/B"],"dc:type":["text"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:25:14Z"}