{"id":{"repo_id":"mit","oai_identifier":"oai:dspace.mit.edu:1721.1/113549"},"canonical_url":"https://search.dev.ndltd.org/etd/mit/oai:dspace.mit.edu:1721.1/113549","repository":{"repo_id":"mit","name":"MIT","base_url":"https://dspace.mit.edu/oai/request"},"display":{"title":"Computing the Lusztig-Vogan bijection","abstract":"Let G be a connected complex reductive algebraic group with Lie algebra g. The Lusztig-Vogan bijection relates two bases for the bounded derived category of G-equivariant coherent sheaves on the nilpotent cone 11 of g. One basis is indexed by ..., the set of dominant weights of G, and the other by [Omega], the set of pairs ... consisting of a nilpotent orbit ... and an irreducible G-equivariant vector bundle ... The existence of the Lusztig-Vogan bijection ... was proven by Bezrukavnikov, and an algorithm computing [gamma] in type A was given by Achar. Herein we present a combinatorial description of [gamma] in type A that subsumes and dramatically simplifies Achar's algorithm.","abstract_html":"Let G be a connected complex reductive algebraic group with Lie algebra g. The Lusztig-Vogan bijection relates two bases for the bounded derived category of G-equivariant coherent sheaves on the nilpotent cone 11 of g. One basis is indexed by ..., the set of dominant weights of G, and the other by [Omega], the set of pairs ... consisting of a nilpotent orbit ... and an irreducible G-equivariant vector bundle ... The existence of the Lusztig-Vogan bijection ... was proven by Bezrukavnikov, and an algorithm computing [gamma] in type A was given by Achar. Herein we present a combinatorial description of [gamma] in type A that subsumes and dramatically simplifies Achar's algorithm.","abstract_has_math":false,"creators":["Rush, David B., Ph. D. Massachusetts Institute of Technology"],"institution":"Massachusetts Institute of Technology","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":"Massachusetts Institute of Technology. Department of Mathematics.","school":null,"contributors":[],"advisors":["David A. Vogan Jr."],"committee_chairs":[],"committee_members":[],"year":2017,"date_issued":"2017","date_published":"2017","updated_at":"2026-07-22T22:21:36Z","subjects":["Mathematics."],"languages":["eng"],"rights":["MIT theses are protected by copyright. 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They may be viewed, downloaded, or printed from this source but further reproduction or distribution in any format is prohibited without written permission."]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://dspace.mit.edu/handle/1721.1/7582"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/1721.1/113549"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2017.","Cataloged from PDF version of thesis.","Includes bibliographical references (pages 129-130)."]},{"key":"dc:description.abstract","label":"Abstract","values":["Let G be a connected complex reductive algebraic group with Lie algebra g. The Lusztig-Vogan bijection relates two bases for the bounded derived category of G-equivariant coherent sheaves on the nilpotent cone 11 of g. One basis is indexed by ..., the set of dominant weights of G, and the other by [Omega], the set of pairs ... consisting of a nilpotent orbit ... and an irreducible G-equivariant vector bundle ... The existence of the Lusztig-Vogan bijection ... was proven by Bezrukavnikov, and an algorithm computing [gamma] in type A was given by Achar. Herein we present a combinatorial description of [gamma] in type A that subsumes and dramatically simplifies Achar's algorithm."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Ph. D."]},{"key":"dc:title","label":"Title","values":["Computing the Lusztig-Vogan bijection"]}]}],"canonical_facts":{"dc:contributor.advisor":["David A. Vogan Jr."],"dc:contributor.department":["Massachusetts Institute of Technology. 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The existence of the Lusztig-Vogan bijection ... was proven by Bezrukavnikov, and an algorithm computing [gamma] in type A was given by Achar. Herein we present a combinatorial description of [gamma] in type A that subsumes and dramatically simplifies Achar's algorithm."],"dc:description.degree":["Ph. D."],"dc:identifier.uri":["http://hdl.handle.net/1721.1/113549"],"dc:language.iso":["eng"],"dc:publisher":["Massachusetts Institute of Technology"],"dc:rights":["MIT theses are protected by copyright. They may be viewed, downloaded, or printed from this source but further reproduction or distribution in any format is prohibited without written permission."],"dc:rights.uri":["http://dspace.mit.edu/handle/1721.1/7582"],"dc:subject":["Mathematics."],"dc:title":["Computing the Lusztig-Vogan bijection"],"dc:type":["Thesis"]},"updated_at":"2026-07-22T22:21:36Z"}