{"id":{"repo_id":"mit","oai_identifier":"oai:dspace.mit.edu:1721.1/126936"},"canonical_url":"https://search.dev.ndltd.org/etd/mit/oai:dspace.mit.edu:1721.1/126936","repository":{"repo_id":"mit","name":"MIT","base_url":"https://dspace.mit.edu/oai/request"},"display":{"title":"Stable characters for symmetric groups and wreath products","abstract":"Given a Hopf algebra R, the Grothendieck group of C = R-mod inherits the structure of a ring. We define a ring [mathematical equation]), which is \"the [mathematical equation] limit\" of the Grothendieck rings of modules for the wreath products [mathematical equation]; it is the Grothendieck group of a certain wreath product Deligne category. The construction yields a basis of [mathematical equation] corresponding to irreducible objects. The structure constants of this basis are stable tensor product multiplicities for the wreath products [mathematical equation]. We generalise [mathematical equation], allowing an arbitrary ring to be substituted for the Grothendieck ring of C. Aside from being a Hopf algebra, [mathematical equation] is the algebra of distributions on a certain affine group scheme. In the special case where C is the category of vector spaces (over C, say), [mathematical equation] is the ring of symmetric functions. The basis obtained by our construction is the family of stable Specht polynomials, which is closely related to the problem of calculating restriction multiplicities from [mathematical equation]. We categorify the stable Specht polynomials by producing a resolution of irreducible representations of S[subscript n] by modules restricted from [mathematical equation].","abstract_html":"Given a Hopf algebra R, the Grothendieck group of C = R-mod inherits the structure of a ring. We define a ring [mathematical equation]), which is "the [mathematical equation] limit" of the Grothendieck rings of modules for the wreath products [mathematical equation]; it is the Grothendieck group of a certain wreath product Deligne category. The construction yields a basis of [mathematical equation] corresponding to irreducible objects. The structure constants of this basis are stable tensor product multiplicities for the wreath products [mathematical equation]. We generalise [mathematical equation], allowing an arbitrary ring to be substituted for the Grothendieck ring of C. Aside from being a Hopf algebra, [mathematical equation] is the algebra of distributions on a certain affine group scheme. In the special case where C is the category of vector spaces (over C, say), [mathematical equation] is the ring of symmetric functions. The basis obtained by our construction is the family of stable Specht polynomials, which is closely related to the problem of calculating restriction multiplicities from [mathematical equation]. We categorify the stable Specht polynomials by producing a resolution of irreducible representations of S[subscript n] by modules restricted from [mathematical equation].","abstract_has_math":false,"creators":["Ryba, Christopher(Christopher Jonathan)"],"institution":"Massachusetts Institute of Technology","degree_name":"Doctoral","degree_level":null,"degree_discipline":null,"degree_department":"Massachusetts Institute of Technology. Department of Mathematics","school":null,"contributors":[],"advisors":["Pavel Etingof."],"committee_chairs":[],"committee_members":[],"year":2020,"date_issued":"2020","date_published":"2020","updated_at":"2026-07-22T22:21:10Z","subjects":["Mathematics."],"languages":["eng"],"rights":["MIT theses may be protected by copyright. Please reuse MIT thesis content according to the MIT Libraries Permissions Policy, which is available through the URL provided."],"rights_urls":["http://dspace.mit.edu/handle/1721.1/7582"],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/1721.1/126936","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Pavel Etingof."]},{"key":"dc:contributor.department","label":"Department","values":["Massachusetts Institute of Technology. Department of Mathematics","Math"]},{"key":"dc:contributor.other","label":"Dc Contributor Other","values":["Massachusetts Institute of Technology. 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We define a ring [mathematical equation]), which is \"the [mathematical equation] limit\" of the Grothendieck rings of modules for the wreath products [mathematical equation]; it is the Grothendieck group of a certain wreath product Deligne category. The construction yields a basis of [mathematical equation] corresponding to irreducible objects. The structure constants of this basis are stable tensor product multiplicities for the wreath products [mathematical equation]. We generalise [mathematical equation], allowing an arbitrary ring to be substituted for the Grothendieck ring of C. Aside from being a Hopf algebra, [mathematical equation] is the algebra of distributions on a certain affine group scheme. In the special case where C is the category of vector spaces (over C, say), [mathematical equation] is the ring of symmetric functions. The basis obtained by our construction is the family of stable Specht polynomials, which is closely related to the problem of calculating restriction multiplicities from [mathematical equation]. We categorify the stable Specht polynomials by producing a resolution of irreducible representations of S[subscript n] by modules restricted from [mathematical equation]."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Ph. D."]},{"key":"dc:title","label":"Title","values":["Stable characters for symmetric groups and wreath products"]}]}],"canonical_facts":{"dc:contributor.advisor":["Pavel Etingof."],"dc:contributor.department":["Massachusetts Institute of Technology. Department of Mathematics","Math"],"dc:contributor.other":["Massachusetts Institute of Technology. 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The structure constants of this basis are stable tensor product multiplicities for the wreath products [mathematical equation]. We generalise [mathematical equation], allowing an arbitrary ring to be substituted for the Grothendieck ring of C. Aside from being a Hopf algebra, [mathematical equation] is the algebra of distributions on a certain affine group scheme. In the special case where C is the category of vector spaces (over C, say), [mathematical equation] is the ring of symmetric functions. The basis obtained by our construction is the family of stable Specht polynomials, which is closely related to the problem of calculating restriction multiplicities from [mathematical equation]. We categorify the stable Specht polynomials by producing a resolution of irreducible representations of S[subscript n] by modules restricted from [mathematical equation]."],"dc:description.degree":["Ph. D."],"dc:identifier.uri":["https://hdl.handle.net/1721.1/126936"],"dc:language.iso":["eng"],"dc:publisher":["Massachusetts Institute of Technology"],"dc:rights":["MIT theses may be protected by copyright. Please reuse MIT thesis content according to the MIT Libraries Permissions Policy, which is available through the URL provided."],"dc:rights.uri":["http://dspace.mit.edu/handle/1721.1/7582"],"dc:subject":["Mathematics."],"dc:title":["Stable characters for symmetric groups and wreath products"],"dc:type":["Thesis"],"thesis:degree_name":["Doctoral"]},"updated_at":"2026-07-22T22:21:10Z"}