Hello Everyone,

I am wondring if I can  find the StandardRepresentation of a subalgebra of simple Lie algebra?

For example I have this code:

with(DifferentialGeometry);
with(LieAlgebras);
with(Library);
with(LinearAlgebra);

G := SimpleLieAlgebraData("sl(6)", sl6);
DGsetup(G);
StandardRepresentation(sl6);
M3 := MinimalSubalgebra([e30, e35, e20]);
B3 := LieAlgebraData(M3, p62);
Query("Jacobi");
DGsetup(B3);
StandardRepresentation(p62);
Error, (in DifferentialGeometry:-LieAlgebras:-StandardRepresentation) expected a Lie algebra constructed by the procedure SimpleLieAlgebraData
 

For the first StandardRepresentation(sl6); it works becouse of the definition. Now what I want the same idea for the subalgebra. How can I do that?

 For the command LieAlgebras[RootSpaceDecomposition] I don't understand what the command return, I read the help and see the examples but still not understanding.

for example it returns:

RSD := RootSpaceDecomposition(CSA);

RSD := table([[-2, -1] = E31, [2, 1] = E13, [1, 2] = E23, [1, -1] = E12, [-1, 1] = E21, [-1, -2] = E32])

I don't understand what means [-2, -1] even they said that is the root but I know that a root is in h* so it must be only a number not a vector.