Graphical Tensor Product Reduction Scheme for the Lie Algebras so(5) = sp(2), su(3), and g(2)

Vlasii, Nadiia Dmytrivna; von Rütte, F.; Wiese, Uwe-Jens (2016). Graphical Tensor Product Reduction Scheme for the Lie Algebras so(5) = sp(2), su(3), and g(2). Annals of physics, 371, pp. 199-227. Elsevier 10.1016/j.aop.2016.03.014

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We develop in detail a graphical tensor product reduction scheme, first described by Antoine and Speiser, for the simple rank 2 Lie algebras so(5) = sp(2), su(3), and g(2). This leads to an efficient practical method to reduce tensor products of irreducible representations into sums of such representations. For this purpose, the 2-dimensional weight diagram of a given representation is placed in a ‘‘landscape’’ of irreducible representations. We provide both the landscapes and the weight diagrams for a large number of representations for the three simple rank 2 Lie algebras. We also apply the algebraic ‘‘girdle’’ method, which is much less efficient for calculations by hand for moderately large representations. Computer code for reducing tensor products, based on the graphical method, has been developed as well and is available from the authors upon request.

Item Type:

Journal Article (Original Article)

Division/Institute:

10 Strategic Research Centers > Albert Einstein Center for Fundamental Physics (AEC)
08 Faculty of Science > Institute of Theoretical Physics

UniBE Contributor:

Vlasii, Nadiia Dmytrivna and Wiese, Uwe-Jens

Subjects:

500 Science > 530 Physics

ISSN:

0003-4916

Publisher:

Elsevier

Language:

English

Submitter:

Esther Fiechter

Date Deposited:

08 Aug 2016 13:46

Last Modified:

08 Aug 2016 13:46

Publisher DOI:

10.1016/j.aop.2016.03.014

ArXiv ID:

1511.02015

BORIS DOI:

10.7892/boris.85279

URI:

https://boris.unibe.ch/id/eprint/85279

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