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dc.contributor.advisorPickrell, Dougen_US
dc.contributor.authorPittman-Polletta, Benjamin Rafael
dc.creatorPittman-Polletta, Benjamin Rafaelen_US
dc.date.accessioned2011-12-05T22:29:35Z
dc.date.available2011-12-05T22:29:35Z
dc.date.issued2010en_US
dc.identifier.urihttp://hdl.handle.net/10150/194348
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.
dc.language.isoenen_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.subjectaffine weyl groupsen_US
dc.subjectbirkhoff factorizationen_US
dc.subjectloop groupsen_US
dc.subjectreduced wordsen_US
dc.subjecttriangular factorizationen_US
dc.titleFactorization in unitary loop groups and reduced words in affine Weyl groups.en_US
dc.typetexten_US
dc.typeElectronic Dissertationen_US
dc.contributor.chairPickrell, Dougen_US
dc.identifier.oclc752261124en_US
thesis.degree.grantorUniversity of Arizonaen_US
thesis.degree.leveldoctoralen_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
thesis.degree.disciplineApplied Mathematicsen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.namePh.D.en_US
refterms.dateFOA2018-06-29T07:28:25Z
html.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.


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