Tensor Product Decomposition in Lie Algebra Representation Theory
(2011) In Master Thesis in Mathematical Science MATM01 20111Mathematics (Faculty of Sciences)
 Abstract
 The basic theory of semisimple Lie algebras and their representations is studied in detail. In particular it is shown that every irreducible module V (λ) is uniquely determined up to isomorphism by its highest weight λ. Then the problem of decomposing a tensor product of two finite dimensional modules into a direct sum of irreducible modules is considered. It is shown that for λ fixed, the decompositions of V (λ) V (μ) for a finite set of μ’s are sufficient to obtain all such decompositions. Some decomposition formulas are given, in particular a geometric method is presented along with several examples.
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/studentpapers/record/2517806
 author
 Nilsson, Jonathan
 supervisor

 Arne Meurman ^{LU}
 organization
 course
 MATM01 20111
 year
 2011
 type
 H2  Master's Degree (Two Years)
 subject
 publication/series
 Master Thesis in Mathematical Science
 report number
 LUNFMA30612011
 ISSN
 14046342
 other publication id
 2011:E5
 language
 English
 id
 2517806
 date added to LUP
 20141215 14:27:05
 date last changed
 20141215 14:27:05
@misc{2517806, abstract = {The basic theory of semisimple Lie algebras and their representations is studied in detail. In particular it is shown that every irreducible module V (λ) is uniquely determined up to isomorphism by its highest weight λ. Then the problem of decomposing a tensor product of two finite dimensional modules into a direct sum of irreducible modules is considered. It is shown that for λ fixed, the decompositions of V (λ) V (μ) for a finite set of μ’s are sufficient to obtain all such decompositions. Some decomposition formulas are given, in particular a geometric method is presented along with several examples.}, author = {Nilsson, Jonathan}, issn = {14046342}, language = {eng}, note = {Student Paper}, series = {Master Thesis in Mathematical Science}, title = {Tensor Product Decomposition in Lie Algebra Representation Theory}, year = {2011}, }