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Categorification of tensor powers of the vector representation of Uq(gl(1|1))

dc.contributor.advisorStroppel, Catharina
dc.contributor.authorSartori, Antonio
dc.date.accessioned2020-04-19T22:49:47Z
dc.date.available2020-04-19T22:49:47Z
dc.date.issued17.06.2014
dc.identifier.urihttps://hdl.handle.net/20.500.11811/6104
dc.description.abstractWe consider the monoidal subcategory of finite-dimensional representations of Uq(gl(1|1)) generated by the vector representation, and we provide a graphical calculus for the intertwining operators, which enables to compute explicitly the canonical basis, as well as the action of Uq(gl(1|1)). We construct a categorification using graded subquotient categories of the BGG category O(gln) and graded functors between them (translation, Zuckermann’s and coapproximation functors). We describe then the regular blocks of these categories as modules over explicit diagram algebras, which are defined using Soergel modules and combinatorics of symmetric polynomials. We construct diagrammatically standard and proper standard modules for the properly stratified structure of these algebras.
dc.language.isoeng
dc.rightsIn Copyright
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/
dc.subjectDarstellungstheorie
dc.subjectQuantum-Gruppen
dc.subjectAlexander-Polynom
dc.subjectKategorie O
dc.subjectLie-Algebren
dc.subjectRepresentation theory
dc.subjectQuantum groups
dc.subjectAlexander polynomial
dc.subjectCategory O
dc.subjectLie algebras
dc.subject.ddc510 Mathematik
dc.titleCategorification of tensor powers of the vector representation of Uq(gl(1|1))
dc.typeDissertation oder Habilitation
dc.publisher.nameUniversitäts- und Landesbibliothek Bonn
dc.publisher.locationBonn
dc.rights.accessRightsopenAccess
dc.identifier.urnhttps://nbn-resolving.org/urn:nbn:de:hbz:5n-36359
ulbbn.pubtypeErstveröffentlichung
ulbbnediss.affiliation.nameRheinische Friedrich-Wilhelms-Universität Bonn
ulbbnediss.affiliation.locationBonn
ulbbnediss.thesis.levelDissertation
ulbbnediss.dissID3635
ulbbnediss.date.accepted30.05.2014
ulbbnediss.instituteMathematisch-Naturwissenschaftliche Fakultät : Fachgruppe Mathematik / Mathematisches Institut
ulbbnediss.fakultaetMathematisch-Naturwissenschaftliche Fakultät
dc.contributor.coRefereeMazorchuk, Volodymyr


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