{"id":{"repo_id":"columbia-diss","oai_identifier":"oai:academiccommons.columbia.edu:10.7916/D8C82H96"},"canonical_url":"https://search.dev.ndltd.org/etd/columbia-diss/oai:academiccommons.columbia.edu:10.7916/D8C82H96","repository":{"repo_id":"columbia-diss","name":"Columbia University","base_url":"https://academiccommons.columbia.edu/oai"},"display":{"title":"Soergel Diagrammatics for Dihedral Groups","abstract":"We give a diagrammatic presentation for the category of Soergel bimodules for the dihedral group W, finite or infinite. The (two-colored) Temperley-Lieb category is embedded inside this category as the degree 0 morphisms between color-alternating objects. The indecomposable Soergel bimodules are the images of Jones-Wenzl projectors. When W is finite, the Temperley-Lieb category must be taken at an appropriate root of unity, and the negligible Jones-Wenzl projector yields the Soergel bimodule for the longest element of W.","abstract_html":"We give a diagrammatic presentation for the category of Soergel bimodules for the dihedral group W, finite or infinite. The (two-colored) Temperley-Lieb category is embedded inside this category as the degree 0 morphisms between color-alternating objects. The indecomposable Soergel bimodules are the images of Jones-Wenzl projectors. When W is finite, the Temperley-Lieb category must be taken at an appropriate root of unity, and the negligible Jones-Wenzl projector yields the Soergel bimodule for the longest element of W.","abstract_has_math":false,"creators":["Elias, Ben"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011","date_published":"2011","updated_at":"2026-07-24T01:44:13Z","subjects":["Mathematics","Hecke algebras","Weyl groups"],"languages":["English"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://doi.org/10.7916/D8C82H96","outbound_label":"DOI","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Elias, Ben"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2011"]},{"key":"dc:type","label":"Dc Type","values":["Theses"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics","Hecke algebras","Weyl groups"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["English"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://doi.org/10.7916/D8C82H96"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["We give a diagrammatic presentation for the category of Soergel bimodules for the dihedral group W, finite or infinite. The (two-colored) Temperley-Lieb category is embedded inside this category as the degree 0 morphisms between color-alternating objects. The indecomposable Soergel bimodules are the images of Jones-Wenzl projectors. When W is finite, the Temperley-Lieb category must be taken at an appropriate root of unity, and the negligible Jones-Wenzl projector yields the Soergel bimodule for the longest element of W."]},{"key":"dc:title","label":"Title","values":["Soergel Diagrammatics for Dihedral Groups"]}]}],"canonical_facts":{"dc:creator":["Elias, Ben"],"dc:date":["2011"],"dc:description":["We give a diagrammatic presentation for the category of Soergel bimodules for the dihedral group W, finite or infinite. The (two-colored) Temperley-Lieb category is embedded inside this category as the degree 0 morphisms between color-alternating objects. The indecomposable Soergel bimodules are the images of Jones-Wenzl projectors. When W is finite, the Temperley-Lieb category must be taken at an appropriate root of unity, and the negligible Jones-Wenzl projector yields the Soergel bimodule for the longest element of W."],"dc:identifier":["https://doi.org/10.7916/D8C82H96"],"dc:language":["English"],"dc:subject":["Mathematics","Hecke algebras","Weyl groups"],"dc:title":["Soergel Diagrammatics for Dihedral Groups"],"dc:type":["Theses"]},"updated_at":"2026-07-24T01:44:13Z"}