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Representation rings of semidirect products of tori by finite groups Stykow, Maxim
Abstract
This dissertation studies semidirect products of a torus by a finite group from the representation theory point of view. The finite group of greatest interest is the cyclic group of prime order. Such semidirect products occur in nature as isotropy groups of Lie groups acting on themselves by conjugation and as normalizers of maximal tori in reductive linear algebraic groups. The main results of this dissertation are: a) the calculation of the representation ring of such semidirect products as an algebra over the integers for certain special cases, b) the adaptation of an algorithm from invariant theory to find finite presentations of representation rings, c) the computation of the topological K-theory of the classifying space of certain semidirect products, d) the demonstration that the equivariant K-theory of the projective unitary group of degree 2 acting on itself by conjugation is not a free module over its representation ring.
Item Metadata
Title |
Representation rings of semidirect products of tori by finite groups
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Creator | |
Publisher |
University of British Columbia
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Date Issued |
2015
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Description |
This dissertation studies semidirect products of a torus by a finite group from the representation theory point of view. The finite group of greatest interest is the cyclic group of prime order. Such semidirect products occur in nature as isotropy groups of Lie groups acting on themselves by conjugation and as normalizers of maximal tori in reductive linear algebraic groups. The main results of this dissertation are: a) the calculation of the representation ring of such semidirect products as an algebra over the integers for certain special cases, b) the adaptation of an algorithm from invariant theory to find finite presentations of representation rings, c) the computation of the topological K-theory of the classifying space of certain semidirect products, d) the demonstration that the equivariant K-theory of the projective unitary group of degree 2 acting on itself by conjugation is not a free module over its representation ring.
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Genre | |
Type | |
Language |
eng
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Date Available |
2015-08-18
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution 2.5 Canada
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DOI |
10.14288/1.0166571
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URI | |
Degree | |
Program | |
Affiliation | |
Degree Grantor |
University of British Columbia
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Graduation Date |
2015-09
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Campus | |
Scholarly Level |
Graduate
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Rights URI | |
Aggregated Source Repository |
DSpace
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Rights
Attribution 2.5 Canada