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Projection operators for simple lie groups
Theoretical and Mathematical Physics, 1971Summary: The solution of many problems in nuclear theory and elementary particle physics amounts to decomposing the reducible representations of the symmetry groups of quantum mechanical systems into irreducible components. To carry out this decomposition, projection operators are needed. In the present paper we have constructed, for all simple compact
Asherova, R. M. +2 more
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Isoparity and Simple Lie Group
Journal of Mathematical Physics, 1967The direct generalization of the isoparity (or G-parity), with the defining property that it is commutable with the referring internal symmetry group, is investigated on the basis of the theory of Lie algebra. This is one special problem of the group extension of a simple Lie group by an involution.
Tanabe, Kosai, Shima, Kazuhisa
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Embedding of a Simple Lie Group into a Simple Lie Group and Branching Rules
Journal of Mathematical Physics, 1967A criterion established by Dynkin is used to specify the embedding of a connected simple Lie group G′ into a connected simple Lie group G, and to derive a standard procedure for evaluating branching rules. It is shown that the weight systems of the irreducible parts contained in the representation of G′ induced by a given finite dimensional ...
Navon, A., Patera, J.
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Representations of simple lie groups
Reports on Mathematical Physics, 1993It is known that the real homology \(H_ * (G)\) of a compact Lie group \(G\) is a Cartesian product of certain odd-dimensional spheres. In the author's interpretation, the group itself can be viewed as a ``twisted'' product of the same spheres: for instance, \(SU(3) \sim S^ 3 \times S^ 5\) is interpreted as the existence of the principal bundle \(SU(2)
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