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dc.contributor.advisorHunziker, Markus.
dc.creatorArmour, David N., 1991-
dc.date.accessioned2018-09-07T13:35:54Z
dc.date.available2018-09-07T13:35:54Z
dc.date.created2018-08
dc.date.issued2018-07-13
dc.date.submittedAugust 2018
dc.identifier.urihttp://hdl.handle.net/2104/10439
dc.description.abstractLet (g,k) be the pair of complexified Lie algebras corresponding to an irreducible Hermitian symmetric space of noncompact type. Then we have an associated triangular decomposition g = p− ⊕ k ⊕ p+, and q = k ⊕ p+ is a maximal parabolic subalgebra of g with abelian nilradical. Associated to the pair (g,q) we can define a highest weight category O(g,q) which is a parabolic analogue of the BGG category O. Each block in O(g,q) contains finitely many simple modules, whose highest weights form a nice partially ordered set. In this thesis a new notion, similarity of blocks, is introduced. Then, for the classical Hermitian symmetric pairs that are in the dual pair setting, a result is proved in each of the three classical cases that every block in O(g,q) is similar to some regular integral block. As an application of similarity, a foray into classical invariant theory leads to a “wonderful correspondence” between certain modules of covariants. This correspondence, which was previously introduced for a few special cases, is extended to all modules of covariants (in the classical cases) that are Cohen-Macaulay.
dc.format.mimetypeapplication/pdf
dc.language.isoen
dc.subjectLie algebras. Category O. Block. Invariant theory. Modules of covariants.
dc.titleSimilarity of blocks in parabolic category O and a wonderful correspondence for modules of covariants.
dc.typeThesis
dc.rights.accessrightsWorldwide access.
dc.type.materialtext
thesis.degree.namePh.D.
thesis.degree.departmentBaylor University. Dept. of Mathematics.
thesis.degree.grantorBaylor University
thesis.degree.levelDoctoral
dc.date.updated2018-09-07T13:35:55Z
dc.creator.orcid0000-0003-2858-1719


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