{"id":{"repo_id":"tdl","oai_identifier":"oai:tdl-ir.tdl.org:2104/7943"},"canonical_url":"https://search.dev.ndltd.org/etd/tdl/oai:tdl-ir.tdl.org:2104/7943","repository":{"repo_id":"tdl","name":"Texas Digital Library","base_url":"https://tdl-ir.tdl.org/server/oai/request"},"display":{"title":"Diagrams and reduced decompositions for cominuscule flag varieties and affine Grassmannians.","abstract":"We develop a system of canonical reduced decompositions of minimal coset representatives of quotients corresponding to cominuscule flag varieties and affine Grassmannians. This canonical decomposition allows, in the first case, an abbreviated computation of relative R-polynomials. From this, we show that these polynomials can be obtained from unlabelled intervals, and more generally, that Kazhdan-Lusztig polynomials associated to cominuscule flag varieties are combinatorially invariant. In the second case, we are able to provide a list of the rationally smooth Schubert varieties in simply laced affine Grassmannians corresponding to types A, D, and E. The results in this case were obtained independently by Billey and Mitchell in 2008.","abstract_html":"We develop a system of canonical reduced decompositions of minimal coset representatives of quotients corresponding to cominuscule flag varieties and affine Grassmannians. This canonical decomposition allows, in the first case, an abbreviated computation of relative R-polynomials. From this, we show that these polynomials can be obtained from unlabelled intervals, and more generally, that Kazhdan-Lusztig polynomials associated to cominuscule flag varieties are combinatorially invariant. In the second case, we are able to provide a list of the rationally smooth Schubert varieties in simply laced affine Grassmannians corresponding to types A, D, and E. The results in this case were obtained independently by Billey and Mitchell in 2008.","abstract_has_math":false,"creators":["Pruett, W. Andrew."],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":["Hunziker, Markus, 1968-"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2010,"date_issued":"2010-06","date_published":"2010-06","updated_at":"2026-07-27T21:19:37Z","subjects":["R-polynomials.","Rational smoothness.","Affine Grassmannians.","Relative R polynomials.","Cominuscule flag varieties.","Combinatorial invariance.","Weyl group quotients."],"languages":["en"],"rights":["Worldwide access","Baylor University theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. 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They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. Contact libraryquestions@baylor.edu for inquiries about permission."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://hdl.handle.net/2104/7943"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/2104/7943"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["We develop a system of canonical reduced decompositions of minimal coset representatives of quotients corresponding to cominuscule flag varieties and affine Grassmannians. This canonical decomposition allows, in the first case, an abbreviated computation of relative R-polynomials. From this, we show that these polynomials can be obtained from unlabelled intervals, and more generally, that Kazhdan-Lusztig polynomials associated to cominuscule flag varieties are combinatorially invariant. In the second case, we are able to provide a list of the rationally smooth Schubert varieties in simply laced affine Grassmannians corresponding to types A, D, and E. The results in this case were obtained independently by Billey and Mitchell in 2008."]},{"key":"dc:title","label":"Title","values":["Diagrams and reduced decompositions for cominuscule flag varieties and affine Grassmannians."]}]}],"canonical_facts":{"dc:contributor":["Hunziker, Markus, 1968-"],"dc:creator":["Pruett, W. Andrew."],"dc:date.accessioned":["2010-06-23T12:23:43Z","2026-02-10T23:03:54Z"],"dc:date.available":["2010-06-23T12:23:43Z"],"dc:date.issued":["2010-06"],"dc:description.abstract":["We develop a system of canonical reduced decompositions of minimal coset representatives of quotients corresponding to cominuscule flag varieties and affine Grassmannians. This canonical decomposition allows, in the first case, an abbreviated computation of relative R-polynomials. From this, we show that these polynomials can be obtained from unlabelled intervals, and more generally, that Kazhdan-Lusztig polynomials associated to cominuscule flag varieties are combinatorially invariant. In the second case, we are able to provide a list of the rationally smooth Schubert varieties in simply laced affine Grassmannians corresponding to types A, D, and E. The results in this case were obtained independently by Billey and Mitchell in 2008."],"dc:identifier":["https://hdl.handle.net/2104/7943"],"dc:identifier.uri":["https://hdl.handle.net/2104/7943"],"dc:language":["en"],"dc:rights":["Worldwide access","Baylor University theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. Contact libraryquestions@baylor.edu for inquiries about permission."],"dc:subject":["R-polynomials.","Rational smoothness.","Affine Grassmannians.","Relative R polynomials.","Cominuscule flag varieties.","Combinatorial invariance.","Weyl group quotients."],"dc:title":["Diagrams and reduced decompositions for cominuscule flag varieties and affine Grassmannians."],"dc:type":["Thesis"]},"updated_at":"2026-07-27T21:19:37Z"}