dc.contributor.advisor | Kujawa, Jonathan | |
dc.contributor.author | Brown, Gordon | |
dc.date.accessioned | 2017-11-07T17:40:58Z | |
dc.date.available | 2017-11-07T17:40:58Z | |
dc.date.issued | 2017-12-15 | |
dc.identifier.uri | https://hdl.handle.net/11244/52409 | |
dc.description.abstract | In the first part of this dissertation, we construct a monoidal supercategory whose morphism spaces are spanned by equivalence classes of diagrams called oriented type Q webs, modulo certain relations. We then prove a monoidal superequivalence between this category and the full subcategory of modules over the type Q Lie superalgebra q_n, tensor-generated by the symmetric powers of the natural module and their duals. This affords a diagrammatic presentation by generators and relations of the q_n-morphisms between these modules in terms of webs. The strategy behind the proof is an application of the method of Cautis-Kamnitzer-Morrison to the (q_m,q_n) Howe duality established by Cheng-Wang.
In the second part, we prove a similar result for the so-called spin permutation modules of the Sergeev superalgebra Ser_k, obtaining a diagrammatic description of the Ser_k-morphisms between them in terms of webs. We also develop the combinatorics of supertabloids, and use them to produce a diagrammatic basis for the space of Ser_k-morphisms between any two spin permutation modules in terms of webs. | en_US |
dc.language | en_US | en_US |
dc.subject | Mathematics. | en_US |
dc.title | Webs for Type Q Lie Superalgebras | en_US |
dc.contributor.committeeMember | Brady, Noel | |
dc.contributor.committeeMember | Livingood, Patrick | |
dc.contributor.committeeMember | Roche, Alan | |
dc.contributor.committeeMember | Schmidt, Ralf | |
dc.date.manuscript | 2017-11 | |
dc.thesis.degree | Ph.D. | en_US |
ou.group | College of Arts and Sciences::Department of Mathematics | en_US |