Branching rules for Weyl group orbits of simple Lie algebras B(n), C(n) and D(n)

Details Branching rules for Weyl group orbits of simple Lie algebras B(n), C(n) and D(n) Branching rules for Weyl group orbits of simple Lie algebras B(n), C(n) and D(n)

2011-01-31

arxiv.org/abs/1101.6043v1

Physics

Mathematical Physics

31 pages, accepted in J. Phys. A : Math. Theor

Scientific paper

The orbits of Weyl groups W(B(n)), W(C(n)) and W(D(n)) of the simple Lie algebras B(n), C(n) and D(n) are reduced to the union of the orbits of Weyl groups of the maximal reductive subalgebras of B(n), C(n) and D(n). Matrices transforming points of W(B(n)), W(C(n)) and W(D(n)) orbits into points of subalgebra orbits are listed for all cases n<=8 and for the infinite series of algebra-subalgebra pairs B(n) - B(n-1) x U(1), B(n) - D(n), B(n) - B(n-k) x D(k), B(n) - A(1), C(n) - C(n-k) x C(k), C(n) - A(n-1) x U(1), D(n) - A(n-1) x U(1), D(n) - D(n-1) x U(1), D(n) -B(n-1), D(n) - B(n-k-1) x B(k), D(n) -D(n-k) x D(k). Numerous special cases and examples are shown.

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