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    Similarity of blocks in parabolic category O and a wonderful correspondence for modules of covariants.

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    ARMOUR-DISSERTATION-2018.pdf (352.0Kb)
    David_Armour_copyrightavailavilityform.pdf (776.6Kb)
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    Date
    2018-07-13
    Author
    Armour, David N., 1991-
    0000-0003-2858-1719
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    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.
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    http://hdl.handle.net/2104/10439
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    Copyright © Baylor® University All rights reserved. Legal Disclosures.
    Baylor University Waco, Texas 76798 1-800-BAYLOR-U
    Baylor University Libraries | One Bear Place #97148 | Waco, TX 76798-7148 | 254.710.2112 | Contact: libraryquestions@baylor.edu
    If you find any errors in content, please contact librarywebmaster@baylor.edu
    DSpace software copyright © 2002-2016  DuraSpace
    Contact Us | Send Feedback
    TDL
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    Atmire NV