- #1

Luck0

- 22

- 1

Note that since ##\Lambda## is diagonal, the generators in the expansion ##\Lambda = \lambda_a t_a## must also be diagonal, i.e., they must span the Cartan subalgebra of ##\mathfrak{su}(N)##, meaning that some of the coefficients ##\lambda_a## must be zero. This means that some of the columns of each matrix ##\Omega## will not enter in the sum ##\sum_{a,b}\lambda_b\Omega_{ab}t_a##. My question is, if I look at ##M = \sum_{a,b}\lambda_b\Omega_{ab}t_a## as a change of coordinates, can I still consider ##\Omega## as an element of ##O(N^2-1)##? Clearly, if I write the elements of ##\Omega## that appear in the sum in matrix form, it will be a rectangular matrix, but I don't know if I can complete it with zeros until I get a square matrix, and if I can, I can't see what happens to orthogonality.

Thanks in advance