Symmetric Tensors and Combinatorics for Finite-Dimensional Representations of Symplectic Lie Algebras

Simple item page
dc.contributor.advisorSchmidt, Ralf
dc.creatorMaddox, Julia Louise
dc.date.accessioned2019-04-27T21:24:40Z
dc.date.available2019-04-27T21:24:40Z
dc.date.issued2012
dc.description.abstractFirst, we develop a result using multilinear algebra to prove, in an elementary way, a useful identity between representations of $\mathfrak{sp}(4, \mathbb{C})$, which involves writing any irreducible representation as a formal combination of tensor products of symmetric powers of the standard representation. Once establishing this identity, we employ a combinatorial argument along with this identity to explicitly determine the weight multiplicities of any irreducible representation of $\mathfrak{sp}(4, \mathbb{C})$. While there is already a closed formula for these multiplicities, our approach is more basic and more easily accessible. After determining these multiplicities, we use them to create a method for computing the $L$- and $\varepsilon$-factors of ${\rm Sp}(4)$. Finally, we provide an approach to producing any irreducible representation of any rank $m$ symplectic Lie algebra as a formal combination of tensor products of symmetric powers of the standard representation, including a general formula given an appropriately large highest weight.
dc.format.extent100 pages
dc.format.mediumapplication.pdf
dc.identifier99164301802042
dc.identifier.urihttps://hdl.handle.net/11244/318625
dc.languageen_US
dc.relation.requiresAdobe Acrobat Reader
dc.subjectTensor algebra
dc.subjectLie algebras
dc.subjectCombinatorial analysis
dc.subjectMultilinear algebra
dc.thesis.degreePh.D.
dc.titleSymmetric Tensors and Combinatorics for Finite-Dimensional Representations of Symplectic Lie Algebras
dc.typetext
dc.typedocument
ou.groupCollege of Arts and Sciences::Department of Mathematics

Files

Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
Maddox_ou_0169D_10758.pdf
Size:
412.8 KB
Format:
Adobe Portable Document Format
Download

Collections

OU - Dissertations