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

Abstract

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.

43 pages, 18 figures

References in corpus (7)

• SO(5) Theory of Antiferromagnetism and Superconductivity
• Exceptional Deconfinement in G(2) Gauge Theory
• Exceptional Confinement in G(2) Gauge Theory
• The Deconfinement Phase Transition of Sp(2) and Sp(3) Yang-Mills Theories in 2+1 and 3+1 Dimensions
• Casimir scaling in G(2) lattice gauge theory
• Exceptional thermodynamics: The equation of state of G(2) gauge theory
• Supersymmetric Deformations of G_2 Manifolds from Higher-Order Corrections to String and M-Theory

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