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Open orbits and augmentations of Dynkin diagrams.

Fan, Sin Tsun Edward. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (leaves 85-87). / Abstract also in Chinese. / Chapter 1 --- Introduction --- p.5 / Chapter 1.1 --- Motivation --- p.5 / Chapter 1.2 --- Main results --- p.10 / Chapter 2 --- Preliminaries --- p.14 / Chapter 2.1 --- Z-gradations of Semisimple Lie Algebras --- p.14 / Chapter 2.2 --- Basic Facts about Algebraic Groups --- p.15 / Chapter 3 --- Weight Multiplicity Free Representations and Pre- homogeneous Vector Spaces --- p.18 / Chapter 3.1 --- Weight Multiplicity Free Representations --- p.18 / Chapter 3.2 --- Prehomogeneous Vector Spaces --- p.22 / Chapter 4 --- Augmentations of Dynkin Diagrams --- p.25 / Chapter 5 --- Orbit Finiteness and Prehomogeneity --- p.32 / Chapter 6 --- Termination of Z-grading --- p.36 / Chapter 7 --- Explicit Construction of Generic Elements in Simply- laced Cases --- p.42 / Chapter 8 --- The Ambient Lie Algebras of Parabolic PVS's --- p.47 / Chapter 9 --- PVS's of Twisted Affine Type --- p.52 / Chapter 10 --- "Orbit Structure of (GL2 x SL2m+1,C2 x A2C2m+1)" --- p.55 / Chapter 11 --- Nilvarieties and Generalisation of Open Orbits --- p.59 / Chapter 11.1 --- Nilvarieties and Visible Representations --- p.59 / Chapter 11.2 --- Augmeantations of Affine Dynkin Diagrams --- p.62 / Chapter 11.3 --- Classification of Irreducible Visible Representations --- p.67 / Chapter 12 --- Real Forms of PVS of Parabolic Type --- p.70 / Chapter 12.1 --- Representations of Real Reductive Lie Algebras and Satake Diagrams --- p.70 / Chapter 12.2 --- Real Forms of PVS of Parabolic Type --- p.77 / Chapter 13 --- Tables --- p.81 / Bibliography --- p.85

Identiferoai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_326834
Date January 2009
ContributorsFan, Sin Tsun Edward., Chinese University of Hong Kong Graduate School. Division of Mathematics.
Source SetsThe Chinese University of Hong Kong
LanguageEnglish, Chinese
Detected LanguageEnglish
TypeText, bibliography
Formatprint, 87 leaves : ill. ; 30 cm.
RightsUse of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/)

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