{"id":{"repo_id":"mit","oai_identifier":"oai:dspace.mit.edu:1721.1/43796"},"canonical_url":"https://search.dev.ndltd.org/etd/mit/oai:dspace.mit.edu:1721.1/43796","repository":{"repo_id":"mit","name":"MIT","base_url":"https://dspace.mit.edu/oai/request"},"display":{"title":"Boundaries of K-types in discrete series","abstract":"Abstract: A fundamental problem about irreducible representations of a reductive Lie group G is understanding their restriction to a maximal compact subgroup K. In certain important cases, known as the discrete series, we have a formula that gives the multiplicity of any given irreducible K-representation (or K-type) as an alternating sum. It is not immediately clear from this formula which K-types, indexed by their highest weights, have non-zero multiplicity. Evidence suggests that the collection is very close to a set of lattice points in a noncompact convex polyhedron. In this paper we shall describe a recursive algorithm for finding the boundary facets of this polyhedron.","abstract_html":"Abstract: A fundamental problem about irreducible representations of a reductive Lie group G is understanding their restriction to a maximal compact subgroup K. In certain important cases, known as the discrete series, we have a formula that gives the multiplicity of any given irreducible K-representation (or K-type) as an alternating sum. It is not immediately clear from this formula which K-types, indexed by their highest weights, have non-zero multiplicity. Evidence suggests that the collection is very close to a set of lattice points in a noncompact convex polyhedron. In this paper we shall describe a recursive algorithm for finding the boundary facets of this polyhedron.","abstract_has_math":false,"creators":["Havlíčková, Markéta"],"institution":"Massachusetts Institute of Technology","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":"Massachusetts Institute of Technology. Dept. of Mathematics.","school":null,"contributors":[],"advisors":["Michael J. Hopkins and David A. Vogan."],"committee_chairs":[],"committee_members":[],"year":2008,"date_issued":"2008","date_published":"2008","updated_at":"2026-07-22T22:22:30Z","subjects":["Mathematics."],"languages":["eng"],"rights":["M.I.T. 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. See provided URL for inquiries about permission."],"rights_urls":["http://dspace.mit.edu/handle/1721.1/7582"],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/1721.1/43796","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Michael J. Hopkins and David A. Vogan."]},{"key":"dc:contributor.department","label":"Department","values":["Massachusetts Institute of Technology. Dept. of Mathematics."]},{"key":"dc:contributor.other","label":"Dc Contributor Other","values":["Massachusetts Institute of Technology. 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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. See provided URL for inquiries about 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/1721.1/43796"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2008.","Includes bibliographical references (p. 75-76)."]},{"key":"dc:description.abstract","label":"Abstract","values":["Abstract: A fundamental problem about irreducible representations of a reductive Lie group G is understanding their restriction to a maximal compact subgroup K. In certain important cases, known as the discrete series, we have a formula that gives the multiplicity of any given irreducible K-representation (or K-type) as an alternating sum. It is not immediately clear from this formula which K-types, indexed by their highest weights, have non-zero multiplicity. Evidence suggests that the collection is very close to a set of lattice points in a noncompact convex polyhedron. In this paper we shall describe a recursive algorithm for finding the boundary facets of this polyhedron."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Ph.D."]},{"key":"dc:title","label":"Title","values":["Boundaries of K-types in discrete series"]}]}],"canonical_facts":{"dc:contributor.advisor":["Michael J. Hopkins and David A. Vogan."],"dc:contributor.department":["Massachusetts Institute of Technology. Dept. of Mathematics."],"dc:contributor.other":["Massachusetts Institute of Technology. Dept. of Mathematics."],"dc:creator":["Havlíčková, Markéta"],"dc:date.accessioned":["2008-12-11T18:29:00Z"],"dc:date.available":["2008-12-11T18:29:00Z"],"dc:date.issued":["2008"],"dc:description":["Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2008.","Includes bibliographical references (p. 75-76)."],"dc:description.abstract":["Abstract: A fundamental problem about irreducible representations of a reductive Lie group G is understanding their restriction to a maximal compact subgroup K. In certain important cases, known as the discrete series, we have a formula that gives the multiplicity of any given irreducible K-representation (or K-type) as an alternating sum. It is not immediately clear from this formula which K-types, indexed by their highest weights, have non-zero multiplicity. Evidence suggests that the collection is very close to a set of lattice points in a noncompact convex polyhedron. In this paper we shall describe a recursive algorithm for finding the boundary facets of this polyhedron."],"dc:description.degree":["Ph.D."],"dc:identifier.uri":["http://hdl.handle.net/1721.1/43796"],"dc:language.iso":["eng"],"dc:publisher":["Massachusetts Institute of Technology"],"dc:rights":["M.I.T. 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. See provided URL for inquiries about permission."],"dc:rights.uri":["http://dspace.mit.edu/handle/1721.1/7582"],"dc:subject":["Mathematics."],"dc:title":["Boundaries of K-types in discrete series"],"dc:type":["Thesis"]},"updated_at":"2026-07-22T22:22:30Z"}