Branching rules for Weyl group orbits involving the Lie algebra U(1)

The orbits of Weyl groups W(L) of all simple Lie algebras L are reduced to the union of orbits of the Weyl groups of maximal reductive non-semisimple subalgebras L′ of L, whenever such subalgebras are present. Matrices transforming points of the orbits of W(L) into points of W(L′) orbits are listed...

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Bibliographic Details
Published in:Journal of physics. Conference series 2011-03, Vol.284 (1), p.012043-10
Main Author: Larouche, M
Format: Article
Language:English
Subjects:
Algebra
Infinite series
Lie groups
Orbits
Physics
Unions
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Summary:The orbits of Weyl groups W(L) of all simple Lie algebras L are reduced to the union of orbits of the Weyl groups of maximal reductive non-semisimple subalgebras L′ of L, whenever such subalgebras are present. Matrices transforming points of the orbits of W(L) into points of W(L′) orbits are listed for the infinite series of algebra-subalgebra pairs An ⊃ An−k−1 × Ak × U(1), Bn ⊃ An−1 × U(1), Dn ⊃ An−1 × U(1), Dn ⊃ Dn−1 × U(1), Dn ⊃ Dn−1 × U(1), and for E6 ⊃ E5 × U(1) and E7 ⊃ E6 × U(1). Examples of branching rules are shown for all cases.
ISSN:1742-6596
1742-6588
1742-6596
DOI:10.1088/1742-6596/284/1/012043