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UBC Theses and Dissertations
Arithmetic theory of symmetrizable split maximal Kac-Moody groups Abbaspour Tazehkand, Hesameddin
Abstract
In this thesis we present a reduction theory for the symmetrizable split maximal Kac-Moody groups. However there are many technical difficulties before one can even formulate a reduction theorem. Combining the two main approaches commonly seen in the literature we define a group, first over any field of characteristic zero and then on any commutative ring of characteristic zero. Then we prove a number of structural properties of the group such as representation in the highest weight modules, existence of a Tits system and an Iwasawa decomposition over ℝ and ℂ. Finally we arrive at reduction theory which can only hold for part of the group.
Item Metadata
Title |
Arithmetic theory of symmetrizable split maximal Kac-Moody groups
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Creator | |
Publisher |
University of British Columbia
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Date Issued |
2012
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Description |
In this thesis we present a reduction theory for the symmetrizable split maximal Kac-Moody groups. However there are many technical difficulties before one can even formulate a reduction theorem. Combining the two main approaches commonly seen in the literature we define a group, first over any field of characteristic zero and then on any commutative ring of characteristic zero. Then we prove a number of structural properties of the group such as representation in the highest weight modules, existence of a Tits system and an Iwasawa decomposition over ℝ and ℂ. Finally we arrive at reduction theory which can only hold for part of the group.
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Genre | |
Type | |
Language |
eng
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Date Available |
2013-02-21
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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DOI |
10.14288/1.0073534
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URI | |
Degree | |
Program | |
Affiliation | |
Degree Grantor |
University of British Columbia
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Graduation Date |
2013-05
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Campus | |
Scholarly Level |
Graduate
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Rights URI | |
Aggregated Source Repository |
DSpace
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Rights
Attribution-NonCommercial-NoDerivatives 4.0 International