Alamino
Jun10-04, 01:41 PM
Iīve just started to study superstrings and Iīm working on Polchinskiīs book problems. I come from other area and so Iīm not used to work with group theory what makes a little difficult to me to understand the solution of exercise 1.5. The solution says that the states with m^2 =1/ \alpha ī form complete representations of SO(D-1), D=26. It is because the states are \alpha^{i}_{-2} \vert 0,k>, that are vectors of SO(D-2) and \alpha^{i}_{-1} \alpha^{j}_{-1} \vert 0,k>, that are tensors of SO(D-2) and they add up to a representation of SO(D-1). Iīve been trying to understand this, but I couldnīt yet. Why \alpha^{i}_{-2} \vert 0,k> are vectors of SO(D-2) and why \alpha^{i}_{-1} \alpha^{j}_{-1} \vert 0,k> are tensors of SO(D-2)? I know just the basics of representation theory for Lie Groups. Can anyone help me and explain it? Iīm sorry for such a basic question, but Iīm just a begginer in these matters...