2012/02/15 by Huajun Huang, Hua-Jun Huang, Youning Li +5
Mathematics · Physics and Astronomy · #16S30 #17B10 #17B25 #20C35 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Quantum Physics (quant-ph) #hep-th #math-ph #math.MP #msc:16S30 #msc:17B10 #msc:17B25 #msc:20C35 #quant-ph
paper · pdf · doi:10.48550/arxiv.1202.3347
29 pages, 4 figures
arxiv created 2012/02/15 · openalex publication_date 2012/02/15 · arxiv updated 2012/02/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper various representations of the exceptional Lie algebra G2 are investigated in a purely algebraic manner, and multi-boson/multi-fermion realizations are obtained. Matrix elements of the master representation, which is defined on the space of the universal enveloping algebra of G2, are explicitly determined. From this master representation, different indecomposable representations defined on invariant subspaces or quotient spaces with respect to these invariant subspaces are discussed. Especially, the elementary representations of G2 are investigated in detail, and the corresponding six-boson realization is given. After obtaining explicit forms of all twelve extremal vectors of the elementary representation with the highest weight Λ, all representations with their respective highest weights related to Λ are systematically discussed. For one of these representations the corresponding five-boson realization is constructed. Moreover, a new three-fermion realization from the fundamental representation (0,1) of G2 is constructed also.