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/student-papers/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
- LUNFMA-3061-2011
- ISSN
- 1404-6342
- other publication id
- 2011:E5
- language
- English
- id
- 2517806
- date added to LUP
- 2014-12-15 14:27:05
- date last changed
- 2014-12-15 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 = {{1404-6342}}, language = {{eng}}, note = {{Student Paper}}, series = {{Master Thesis in Mathematical Science}}, title = {{Tensor Product Decomposition in Lie Algebra Representation Theory}}, year = {{2011}}, }