= Dn root system
{c}
{title2=$D_n=\{\pm e_i\pm e_j:i<j\}$}
For the complexified <Special orthogonal Lie algebra> $\mathfrak{so}_{2n}$, $n\geq2$, choose positive <roots of a root system> $e_i-e_j$ and $e_i+e_j$ for $i<j$. Its <Weyl vector> is $\rho=(n-1,n-2,\ldots,0)$. Dominant coordinates satisfy $\lambda_1\geq\cdots\geq\lambda_{n-1}\geq|\lambda_n|$. The <Weyl dimension formula> becomes $\prod_{i<j}((\lambda_i+\rho_i)^2-(\lambda_j+\rho_j)^2)/(\rho_i^2-\rho_j^2)$. The case $D_2$ is two independent <A1 root systems>, while $D_3$ is isomorphic to the <A3 root system>.
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