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Permanent link (DOI): https://doi.org/10.7939/R38C9RB04

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Maximal abelian k-diagonalizable subgroups of reductive groups Open Access

Descriptions

Other title
Subject/Keyword
diagonalizable
reductive group
representation
Type of item
Thesis
Degree grantor
University of Alberta
Author or creator
Tan, Xiaobai
Supervisor and department
Jochen Kuttle (Mathematical and Statistical Sciences)
Arturo Pianzola (Mathematical and Statistical Sciences)
Examining committee member and department
Vladimir Chernousov (Mathematical and Statistical Sciences)
Vincent Bouchard (Mathematical and Statistical Sciences)
Department
Department of Mathematical and Statistical Sciences
Specialization
Mathematics
Date accepted
2014-09-29T08:56:53Z
Graduation date
2014-11
Degree
Doctor of Philosophy
Degree level
Doctoral
Abstract
Given an algebraic group G over a field k and a k-algebra R, the role of maximal abelian k-diagonalizable subalgebras (MAD for short) of G(R) is the same as that the split maximal torus play in G(k). Let G be a reductive group such that the derived subgroup is simply connected and let Spec(R) be a connected reduced affine scheme. This dissertation is to studying conjugacy problems related to MADs in G(R). First, we provide the conjugacy theorem for regular MADs. For arbitrary MADs, the conjugacy theorem does not exist. But we give the structure of MADs in the classical groups of type A;B;C and D.
Language
English
DOI
doi:10.7939/R38C9RB04
Rights
Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of these terms. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.
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