# Beginner´s Question on Bosonic Open Strings

1. Jun 10, 2004

### Alamino

I´ve just started to study superstrings and I´m working on Polchinski´s book problems. I come from other area and so I´m 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 $$m^2 =1/ \alpha ´$$ 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). I´ve been trying to understand this, but I couldn´t 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? I´m sorry for such a basic question, but I´m just a begginer in these matters...