I'm trying to calculate the dimension of the irreducible representation of the SO(5) group with maximum weight equal to $2\lambda_1$. However I must be missing something because according to the books the group has dimension 10 and rank 2, and my calculations are giving dimension 12.
$dim\,D^{\lambda}=\frac{\underset{\alpha>0}{\prod}(\lambda+\delta)\cdot\alpha}{\underset{\alpha>0}{\prod}\delta\cdot\alpha}$, where $\delta=\alpha_{1}+\alpha_{2}$ and $\alpha^{2}=2$
$\delta\,\cdot\,\alpha_{1}=1 \quad\quad\quad \delta\,\cdot\,\alpha_{2}=1 \quad\quad\quad \delta\,\cdot\,\alpha_{3}=2 \quad\quad\quad \delta\,\cdot\,\alpha_{4}=2$
and
$\alpha_{1}\,\cdot\,2\lambda_{1}=2 \quad\quad\quad \alpha_{2}\,\cdot\,2\lambda_{1}=0 \quad\quad\quad \alpha_{3}\,\cdot\,2\lambda_{1}=2 \quad\quad\quad \alpha_{4}\,\cdot\,2\lambda_{1}=2 \quad\quad\quad $
applying in the formula:
$dim\,D^{2\lambda_1}=\frac{((2+1)*(1+0)*(2+2)*(2+2)}{(1)*(1)*(2)*(2)}=\frac{48}{4}=12$
Where am I going wrong ??
