# LUP Student Papers

## LUND UNIVERSITY LIBRARIES

### Tensor Product Decomposition in Lie Algebra Representation Theory

(2011) In Master Thesis in Mathematical Science MATM01 20111
Mathematics (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.
author
supervisor
organization
course
MATM01 20111
year
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
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},
}

```