Character generators and graphs for simple lie algebras

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dc.contributor.authorOkeke, Nnamdi
dc.contributor.authorUniversity of Lethbridge. Faculty of Arts and Science
dc.contributor.supervisorWalton, Mark A.
dc.date.accessioned2007-11-29T16:30:54Z
dc.date.available2007-11-29T16:30:54Z
dc.date.issued2006
dc.degree.levelMasters
dc.descriptionvii, 92 leaves ; 29 cm.en
dc.description.abstractWe study character generating functions (character generators) of simple Lie algebras. The expression due to Patera and Sharp, derived from the Weyl character formula, is ¯rst re- viewed. A new general formula is then found. It makes clear the distinct roles of \outside" and \inside" elements of the integrity basis, and helps determine their quadratic incompati- bilities. We review, analyze and extend the results obtained by Gaskell using the Demazure character formulas. We ¯nd that the fundamental generalized-poset graphs underlying the character generators can be deduced from such calculations. These graphs, introduced by Baclawski and Towber, can be simpli¯ed for the purposes of constructing the character generator. The generating functions can be written easily using the simpli¯ed versions, and associated Demazure expressions. The rank-two algebras are treated in detail, but we believe our results are indicative of those for general simple Lie algebras.en
dc.identifier.urihttps://hdl.handle.net/10133/532
dc.language.isoen_USen
dc.publisherLethbridge, Alta. : University of Lethbridge, Faculty of Arts and Science, 2006en
dc.publisher.departmentDepartment of Physicsen
dc.publisher.facultyFaculty of Arts and Scienceen
dc.relation.ispartofseriesThesis (University of Lethbridge. Faculty of Arts and Science)en
dc.subjectDissertations, Academicen
dc.subjectLie algebras -- Researchen
dc.subjectLie groups -- Researchen
dc.titleCharacter generators and graphs for simple lie algebrasen
dc.typeThesisen
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