I'm trying to find an orthonormal basis for gl(3)-module V(ε1-ε3), where ε1-ε3 is the weight (1,0,-1) of the highest-weight vector. Using Gelfand-Tsetlin (/Zetlin/Zeitlin) patterns, I'm at the point where I have the gl(2) submodules, their dimensions, and the branching pattern. I now need to find the matrix representation for those gl(2) submodules - any help?
My working below...
