M Larouche et al 2009 J. Phys. A: Math. Theor. 42 485203 doi:10.1088/1751-8113/42/48/485203
Branching rules for the Weyl group orbits of the Lie algebra An
M Larouche1, M Nesterenko2 and J Patera1
Show affiliationsThe orbits of Weyl groups W(An) of simple An-type Lie algebras are reduced to the union of orbits of the Weyl groups of maximal reductive subalgebras of An. Matrices transforming points of the orbits of W(An) into points of subalgebra orbits are listed for all cases n ≤ 8 and for the infinite series of algebra–subalgebra pairs An ⊃ An−k−1 × Ak × U1, A2n ⊃ Bn, A2n−1 ⊃ Cn, A2n−1 ⊃ Dn. Numerous special cases and examples are shown.
- PACS
- MSC
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17Bxx Lie algebras and Lie superalgebras (For Lie groups, see 22Exx)
53A07 Higher-dimensional and -codimensional surfaces in Euclidean n-space
20F55 Reflection and Coxeter groups (See also 22E40, 51F15)
22E60 Lie algebras of Lie groups (For the algebraic theory of Lie algebras, see 17Bxx)
- Subjects
- Dates
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Issue 48 (4 December 2009)
Received 14 September 2009, in final form 15 October 2009
Published 11 November 2009
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Branching rules for the Weyl group orbits of the Lie algebra An
M Larouche et al 2009 J. Phys. A: Math. Theor. 42 485203
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