Similarity of blocks in parabolic category O and a wonderful correspondence for modules of covariants.
| dc.contributor.advisor | Hunziker, Markus. | |
| dc.creator | Armour, David N., 1991- | |
| dc.creator.orcid | 0000-0003-2858-1719 | |
| dc.date.accessioned | 2018-09-07T13:35:54Z | |
| dc.date.available | 2018-09-07T13:35:54Z | |
| dc.date.created | 2018-08 | |
| dc.date.issued | 2018-07-13 | |
| dc.date.submitted | August 2018 | |
| dc.date.updated | 2018-09-07T13:35:55Z | |
| dc.description.abstract | Let (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.mimetype | application/pdf | |
| dc.identifier.uri | http://hdl.handle.net/2104/10439 | |
| dc.language.iso | en | |
| dc.rights.accessrights | Worldwide access. | |
| dc.subject | Lie algebras. Category O. Block. Invariant theory. Modules of covariants. | |
| dc.title | Similarity of blocks in parabolic category O and a wonderful correspondence for modules of covariants. | |
| dc.type | Thesis | |
| dc.type.material | text | |
| thesis.degree.department | Baylor University. Dept. of Mathematics. | |
| thesis.degree.grantor | Baylor University | |
| thesis.degree.level | Doctoral | |
| thesis.degree.name | Ph.D. |
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