R C King and A H A Al-Qubanchi 1981 J. Phys. A: Math. Gen. 14 51 doi:10.1088/0305-4470/14/1/007
R C King and A H A Al-Qubanchi
Show affiliationsThe Weyl group, WG, of each exceptional simple Lie group G, is described in detail. Its structure is defined in terms of its coset decomposition with respect to the Weyl group, WH, of a classical semi-simple Lie group, H, embedded naturally in G. The concepts of G-dominance and G-equivalence are defined and used to determine, from the character formula of Weyl, the branching rule associated with the restriction of group elements from G to H. The Weyl group WG is used further to impose constraints on both the branching multiplicities for G to H and the weight multiplicities of G. These constraints are used to evaluate the weight multiplicities of F4, E6, E7 and E8 together with the branching multiplicities for E8 to SO(16).
02.20.Sv Lie algebras of Lie groups
02.20.Qs General properties, structure, and representation of Lie groups
17B20 Simple, semisimple, reductive (super)algebras (roots)
22E60 Lie algebras of Lie groups (For the algebraic theory of Lie algebras, see 17Bxx)
Issue 1 (1 January 1981)
R C King and A H A Al-Qubanchi 1981 J. Phys. A: Math. Gen. 14 51
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