Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
On tensor product of non-unitary representations of sl(2,R)
Karlstad University, Division for Engineering Sciences, Physics and Mathematics.
2007 (English)Independent thesis Advanced level (degree of Magister), 20 points / 30 hpStudent thesis
Abstract [en]

The study of symmetries is an essential tool in modern physics. The analysis of symmetries is often carried out in the form of Lie algebras and their representations. Knowing the representation theory of a Lie algebra includes knowing how tensor products of representations behave. In this thesis two methods to study and decompose tensor products of representations of non-compact Lie algebras are presented and applied to sl(2,R). We focus on products containing non-unitary representations, especially the product of a unitary highest weight representation and a non-unitary finite dimensional. Such products are not necessarily decomposable. Following the theory of B. Kostant we use infinitesimal characters to show that this kind of tensor product is fully reducible iff the sum of the highest weights in the two modules is not a positive integer or zero. The same result is obtained by looking for an invariant coupling between the product module and the contragredient module of some possible submodule. This is done in the formulation by Barut & Fronsdal. From the latter method we also obtain a basis for the submodules consisting of vectors from the product module. The described methods could be used to study more complicated semisimple Lie algebras.

Place, publisher, year, edition, pages
2007. , p. 41
Keywords [en]
sl(2, R), Lie algebra, Representation theory, Tensor product representations, Non-compact algebra, Invariant coupling, Infinitesimal character
National Category
Natural Sciences
Identifiers
URN: urn:nbn:se:kau:diva-1047OAI: oai:DiVA.org:kau-1047DiVA, id: diva2:4815
Presentation
2007-06-21
Uppsok
bio-/geovetenskap
Supervisors
Examiners
Available from: 2007-08-14 Created: 2007-08-14

Open Access in DiVA

fulltext(352 kB)391 downloads
File information
File name FULLTEXT01.pdfFile size 352 kBChecksum MD5
e520b17846c2f3a593aa6c87dd84bb90df873d0ee00b7d61f1a96583277900f097f8488d
Type fulltextMimetype application/pdf

By organisation
Division for Engineering Sciences, Physics and Mathematics
Natural Sciences

Search outside of DiVA

GoogleGoogle Scholar
Total: 391 downloads
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

urn-nbn

Altmetric score

urn-nbn
Total: 415 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf