Produces a module over the direct sum of the Lie algebras of the two modules.
i1 : LL_(1,2,3,4) (simpleLieAlgebra("D",4)) @ LL_(5,6) (simpleLieAlgebra("G",2)) o1 = LL (𝔡 ++ 𝔤 ) 1,2,3,4,5,6 4 2 o1 : irreducible LieAlgebraModule over 𝔡 ++ 𝔤 4 2
A complicated way to define usual tensor product LieAlgebraModule ** LieAlgebraModule would be using the diagonal embedding:
i2 : g := simpleLieAlgebra("A",1) o2 = 𝔞 1 o2 : simple LieAlgebra
i3 : h := g ++ g o3 = 𝔞 ++ 𝔞 1 1 o3 : LieAlgebra
i4 : gdiag := subLieAlgebra(h,matrix {{1},{1}}) o4 = 𝔞 1 o4 : simple LieAlgebra, subalgebra of 𝔞 ++ 𝔞 1 1
i5 : M = LL_5 (g); M' = LL_2 (g);
i7 : M @ M' o7 = LL (𝔞 ++ 𝔞 ) 5,2 1 1 o7 : irreducible LieAlgebraModule over 𝔞 ++ 𝔞 1 1
i8 : branchingRule(oo,gdiag) o8 = LL (𝔞 ) ++ LL (𝔞 ) ++ LL (𝔞 ) 3 1 5 1 7 1 o8 : LieAlgebraModule over 𝔞 1
i9 : M ** M' o9 = LL (𝔞 ) ++ LL (𝔞 ) ++ LL (𝔞 ) 3 1 5 1 7 1 o9 : LieAlgebraModule over 𝔞 1