Factorization in unitary loop groups and reduced words in affine Weyl groups.

Persistent Link:
http://hdl.handle.net/10150/194348
Title:
Factorization in unitary loop groups and reduced words in affine Weyl groups.
Author:
Pittman-Polletta, Benjamin Rafael
Issue Date:
2010
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
The purpose of this dissertation is to elaborate, with specific examples and calculations, on a new refinement of triangular factorization for the loop group of a simple, compact Lie group K, first appearing in Pickrell & Pittman-Polletta 2010. This new factorization allows us to write a smooth map from the unit circle into K (having a triangular factorization) as a triply infinite product of loops, each of which depends on a single complex parameter. These parameters give a set of coordinates on the loop group of K.The order of the factors in this refinement is determined by an infinite sequence of simple generators in the affine Weyl group associated to K, having certain properties. The major results of this dissertation are examples of such sequences for all the classical Weyl groups.We also produce a variation of this refinement which allows us to write smooth maps from the unit circle into the special unitary group of n by n matrices as products of 2n+1 infinite products. By analogy with the semisimple analog of our factorization, we suggest that this variation of the refinement has simpler combinatorics than that appearing in Pickrell & Pittman-Polletta 2010.
Type:
text; Electronic Dissertation
Keywords:
affine weyl groups; birkhoff factorization; loop groups; reduced words; triangular factorization
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Applied Mathematics; Graduate College
Degree Grantor:
University of Arizona
Advisor:
Pickrell, Doug
Committee Chair:
Pickrell, Doug

Full metadata record

DC FieldValue Language
dc.language.isoenen_US
dc.titleFactorization in unitary loop groups and reduced words in affine Weyl groups.en_US
dc.creatorPittman-Polletta, Benjamin Rafaelen_US
dc.contributor.authorPittman-Polletta, Benjamin Rafaelen_US
dc.date.issued2010en_US
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.description.abstractThe purpose of this dissertation is to elaborate, with specific examples and calculations, on a new refinement of triangular factorization for the loop group of a simple, compact Lie group K, first appearing in Pickrell & Pittman-Polletta 2010. This new factorization allows us to write a smooth map from the unit circle into K (having a triangular factorization) as a triply infinite product of loops, each of which depends on a single complex parameter. These parameters give a set of coordinates on the loop group of K.The order of the factors in this refinement is determined by an infinite sequence of simple generators in the affine Weyl group associated to K, having certain properties. The major results of this dissertation are examples of such sequences for all the classical Weyl groups.We also produce a variation of this refinement which allows us to write smooth maps from the unit circle into the special unitary group of n by n matrices as products of 2n+1 infinite products. By analogy with the semisimple analog of our factorization, we suggest that this variation of the refinement has simpler combinatorics than that appearing in Pickrell & Pittman-Polletta 2010.en_US
dc.typetexten_US
dc.typeElectronic Dissertationen_US
dc.subjectaffine weyl groupsen_US
dc.subjectbirkhoff factorizationen_US
dc.subjectloop groupsen_US
dc.subjectreduced wordsen_US
dc.subjecttriangular factorizationen_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineApplied Mathematicsen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorPickrell, Dougen_US
dc.contributor.chairPickrell, Dougen_US
dc.contributor.committeememberPickrell, Dougen_US
dc.contributor.committeememberGlickenstein, Daviden_US
dc.contributor.committeememberPalmer, Johnen_US
dc.contributor.committeememberFlaschka, Hermannen_US
dc.contributor.committeememberVenkataramani, Shankaren_US
dc.identifier.proquest11281en_US
dc.identifier.oclc752261124en_US
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