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dc.contributor.advisorChindris, Calineng
dc.contributor.authorCollins, Breteng
dc.date.issued2018eng
dc.date.submitted2018 Springeng
dc.description.abstractThis thesis is devoted to the combinatorial and geometric study of certain multiplicities, which we call generalized Littlewood-Richardson coefficients. These are sums of products of single Littlewood-Richardson coefficients, and the specific ones we study describe the branching rules for the direct sum and diagonal embeddings of GL(n) as well as the decompositions of extremal weight crystals of type A+. By representing these multiplicities as dimensions of weight spaces of quiver semi-invariants, we use quiver theory to prove their saturation and describe necessary and sufficient conditions for them to be nonzero, culminating in statements similar to Horn's classical conjecture. We then use these conditions to prove various combinatorial properties, including how these multiplicities can be factored and that these numbers in certain cases satisfy the same conjectures as single Littlewood-Richardson coefficients. Finally, we provide a polytopal description of these multiplicities and prove that their positivity can be computed in strongly polynomial time.eng
dc.description.bibrefIncludes bibliographic referenceseng
dc.format.extentvii, 125 pages : illustrationeng]
dc.format.extentvii, 125 pages : illustrationeng]
dc.identifier.urihttps://hdl.handle.net/10355/66149
dc.languageEnglisheng
dc.publisherUniversity of Missouri--Columbiaeng
dc.relation.ispartofcollectionUniversity of Missouri--Columbia. Graduate School. Theses and Dissertationseng
dc.rightsOpenAccesseng
dc.rights.licenseThis work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Licenseeng
dc.titleGeneralized littlewood-richardson coefficients for branching rules of GL(n) and extremal weight crystalseng
dc.typeThesiseng
thesis.degree.disciplineMathematics (MU)eng
thesis.degree.grantorUniversity of Missouri--Columbiaeng
thesis.degree.levelDoctoraleng
thesis.degree.namePh. D.eng


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