Show simple item record

dc.contributor.advisorPavel Etingof.en_US
dc.contributor.authorEntova Aizenbud, Innaen_US
dc.contributor.otherMassachusetts Institute of Technology. Department of Mathematics.en_US
dc.date.accessioned2016-09-30T19:37:47Z
dc.date.available2016-09-30T19:37:47Z
dc.date.copyright2016en_US
dc.date.issued2016en_US
dc.identifier.urihttp://hdl.handle.net/1721.1/104601
dc.descriptionThesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2016.en_US
dc.descriptionCataloged from PDF version of thesis.en_US
dc.descriptionIncludes bibliographical references (pages 207-208).en_US
dc.description.abstractThis thesis gives an analogue to the classical Schur-Weyl duality in the setting of Deligne categories. Given a finite-dimensional unital vector space V (i.e. a vector space V with a distinguished non-zero vector 1) we give a definition of a complex tensor power of V. This is an Ind-object of the Deligne category Rep(St) equipped with a natural action of gl(V). This construction allows us to describe a duality between the abelian envelope of the category Rep(St) and a localization of the category Op/t,v (the parabolic category 0 for gl(V) associated with the pair (V, 1)). In particular, we obtain an exact contravariant functor SWt from the category Repab(St) (the abelian envelope of the category Rep(St)) to a certain quotient of the category Op/t v. This quotient, denoted by 0 p/t v, is obtained by taking the full subcategory of Op/t v consisting of modules of degree t, and localizing by the subcategory of finite dimensional modules. It turns out that the contravariant functor SWt makes Op/t v a Serre quotient of the category Repab(St)OP, and the kernel of SWt can be explicitly described. In the second part of this thesis, we consider the case when V = C[infinity] . We define the appropriate version of the parabolic category 0 and its localization, and show that the latter is equivalent to a "restricted" inverse limit of categories Op/t1CN with N tending to infinity. The Schur-Weyl functors SWt,CN then give an anti-equivalence between the category Op[infinity]/t C[infinity]and the category Repab(Se). This duality provides an unexpected tensor structure on the category Op[infinity]/t C[infinity].en_US
dc.description.statementofresponsibilityby Inna Entova Aizenbud.en_US
dc.format.extent208 pagesen_US
dc.language.isoengen_US
dc.publisherMassachusetts Institute of Technologyen_US
dc.rightsM.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.en_US
dc.rights.urihttp://dspace.mit.edu/handle/1721.1/7582en_US
dc.subjectMathematics.en_US
dc.titleSchur Weyl duality in complex ranken_US
dc.typeThesisen_US
dc.description.degreePh. D.en_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Mathematics.en_US
dc.identifier.oclc958838525en_US


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record